7th Grade Math Quiz
Practice Solve Area And Volume Problems in 7th Grade Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.
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A right triangular prism has a triangular base with legs of 5 cm and 12 cm, and the prism has a height of 8 cm. If the prism is cut by a plane parallel to its triangular base at a height of 3 cm from the bottom, what is the volume of the smaller piece?
This quiz focuses on Solve Area And Volume Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for 7th Grade Math.
Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.
A right triangular prism has a triangular base with legs of 5 cm and 12 cm, and the prism has a height of 8 cm. If the prism is cut by a plane parallel to its triangular base at a height of 3 cm from the bottom, what is the volume of the smaller piece?
Explanation: The triangular base has area ½ × 5 × 12 = 30 sq cm. The smaller piece has the same base area but height of 3 cm. Volume = base area × height = 30 × 3 = 90 cubic cm. Choice B uses height of 4 cm (8-4 error). Choice C uses height of 5 cm (leg length confusion). Choice D uses height of 6 cm (8-2 error).
A cardboard cutout is an irregular polygon that can be decomposed into a rectangle and two right triangles.
What is the total area of the cutout?
Explanation: This problem tests solving area problems for composite figures by decomposing into simpler shapes (rectangles, triangles, prisms, pyramids), applying formulas, and combining results. Formulas: triangle A=(1/2)bh, rectangle A=lw, rectangular prism V=lwh, pyramid V=(1/3)Bh (B=base area), triangular prism V=((1/2)bh)×length (triangle base area times prism length). The cutout has: rectangle area = 8 × 4 = 32 cm², each triangle area = (1/2) × 4 × 3 = 6 cm², two triangles total = 2 × 6 = 12 cm², so total area = 32 + 12 = 44 cm². The correct total area is 44 cm². Common errors include forgetting the (1/2) in triangle area formula (using 4 × 3 = 12 per triangle, giving total 56), or counting only one triangle instead of two. Steps: (1) identify composite structure (rectangle plus two triangles), (2) calculate rectangle area (8 × 4 = 32), (3) calculate one triangle area using A = (1/2)bh = (1/2) × 4 × 3 = 6, (4) multiply by 2 for two congruent triangles (2 × 6 = 12), (5) add all areas (32 + 12 = 44), (6) verify units (cm²).
A cylindrical water tank has a radius of 6 feet and a height of 10 feet. Water is pumped out at a rate such that the water level drops 2 feet per hour. How many cubic feet of water are removed in the first 3 hours?
Explanation: In 3 hours, the water level drops 2 × 3 = 6 feet. The volume of water removed is a cylinder with radius 6 feet and height 6 feet: V = πr²h = π(6²)(6) = 216π cubic feet. Choice B uses height of 10 instead of 6. Choice C doubles the correct answer. Choice D uses the total tank volume incorrectly.
A school display is shaped like a “house”: a rectangle with a triangle on top. The rectangle is 8 in wide and 5 in tall. The triangle on top has the same base as the rectangle (8 in) and height 3 in. What is the total area of the display?
Explanation: This problem tests solving area problems for composite figures by decomposing into simpler shapes (rectangles, triangles, prisms, pyramids), applying formulas, and combining results. Formulas: triangle A=(1/2)bh, rectangle A=lw, rectangular prism V=lwh, pyramid V=(1/3)Bh (B=base area), triangular prism V=((1/2)bh)×length (triangle base area times prism length). The house-shaped display has: rectangle area = 8 × 5 = 40 in², triangle area = (1/2) × 8 × 3 = 12 in², so total area = 40 + 12 = 52 in². The correct total area is 52 in². Common errors include forgetting the (1/2) in the triangle formula (using 8 × 3 = 24, giving total 64), or arithmetic mistakes in addition. Steps: (1) identify composite structure (rectangle with triangle on top), (2) calculate rectangle area (8 × 5 = 40), (3) calculate triangle area using A = (1/2)bh = (1/2) × 8 × 3 = 12, (4) add areas (40 + 12 = 52), (5) verify units (in²). The "house" shape is a common composite figure—remember the triangle on top uses the same base width as the rectangle below.
A triangular prism has a triangular base with base 9 m and height 4 m, and the prism length is 5 m. What is the volume of the prism?
Explanation: This problem tests solving volume problems for composite figures by decomposing into simpler shapes (rectangles, triangles, prisms, pyramids), applying formulas, and combining results. Formulas: triangle A=(1/2)bh, rectangle A=lw, rectangular prism V=lwh, pyramid V=(1/3)Bh (B=base area), triangular prism V=((1/2)bh)×length (triangle base area times prism length). For the triangular prism: triangular base area = (1/2) × 9 × 4 = 18 m², volume = 18 × 5 = 90 m³. The correct volume is 90 m³. Common errors include forgetting the (1/2) in the triangle area formula (using 9 × 4 = 36, giving volume 180), or confusing the prism length with other dimensions. Steps: (1) identify the shape (triangular prism), (2) calculate triangular base area using A = (1/2)bh = (1/2) × 9 × 4 = 18 m², (3) multiply base area by prism length: V = 18 × 5 = 90 m³, (4) verify units (m³). The triangular prism volume formula is (triangular base area) × length—don't forget the (1/2) factor in the triangle area.
An L-shaped classroom floor needs new carpet. The floor can be seen as a large rectangle 10 m×8 m with a rectangular storage cutout 4 m×3 m removed from one corner. What is the area of the floor to be carpeted?
Explanation: This question tests solving area, volume, and surface area problems for composite figures by decomposing into simpler shapes (rectangles, triangles, prisms, pyramids), applying formulas, and combining results. Composite figures: decompose into standard shapes (L-shape as two rectangles: 10×5=50 and 6×3=18, sum: 68; or as large minus cutout: 10×8=80 minus 4×3=12, difference: 68, equivalent). Formulas: triangle A=(1/2)bh, rectangle A=lw, rectangular prism V=lwh, pyramid V=(1/3)Bh (B=base area), triangular prism V=((1/2)bh)×length (triangle base area times prism length). Surface area: sum all face areas (rectangular prism 3×4×5 has faces: two 3×4=12, two 3×5=15, two 4×5=20, total: 2(12+15+20)=94). For this L-shaped floor, decompose as large rectangle 10 m × 8 m = 80 m² minus cutout 4 m × 3 m = 12 m², resulting in 68 m²; alternatively, two rectangles: one 10 m × 5 m = 50 m² and one 6 m × 3 m = 18 m² (assuming the cutout leaves an L with those dimensions), total 68 m². Common errors include calculating the large rectangle only (80 m²), adding instead of subtracting the cutout (92 m²), or wrong decomposition like treating as single shape without adjustment. Steps: (1) identify composite structure (L-shape with cutout), (2) decompose into standard shapes (large rectangle minus small rectangle), (3) calculate each component (apply formulas: A=lw), (4) combine (subtract cutout), (5) verify units (area m²). Decomposition choice: two rectangles OR large-minus-small (both valid, should give same answer—good check).
A science class builds a triangular prism model. The triangular base has base 6 cm and height 4 cm. The prism length is 10 cm. What is the volume of the triangular prism?
Explanation: Tests solving area, volume, and surface area problems for composite figures by decomposing into simpler shapes (rectangles, triangles, prisms, pyramids), applying formulas, and combining results. Composite figures: decompose into standard shapes (L-shape as two rectangles: 10×5=50 and 6×3=18, sum: 68; or as large minus cutout: 10×8=80 minus 4×3=12, difference: 68, equivalent). Formulas: triangle A=(1/2)bh, rectangle A=lw, rectangular prism V=lwh, pyramid V=(1/3)Bh (B=base area), triangular prism V=((1/2)bh)×length (triangle base area times prism length). For this triangular prism, first find the triangular base area: A=(1/2)×6×4=12 cm², then multiply by prism length: V=12×10=120 cm³. Common error would be forgetting the (1/2) in the triangle area formula, using 6×4=24 instead of 12, giving volume 240 cm³. Steps: (1) identify shape (triangular prism), (2) calculate triangular base area using A=(1/2)bh=(1/2)×6×4=12 cm², (3) multiply by prism length for volume V=12×10=120 cm³, (4) verify units (volume in cm³). The key is remembering that triangular prism volume equals (triangular base area)×(prism length), and the triangular area requires the factor (1/2).
A toy block is made by stacking two rectangular prisms. Prism 1 is 6 cm×4 cm×2 cm. Prism 2 is 3 cm×4 cm×2 cm. They are stacked without overlap (their volumes add). What is the total volume of the toy block?
Explanation: This problem tests solving volume problems for composite figures by decomposing into simpler shapes (rectangles, triangles, prisms, pyramids), applying formulas, and combining results. Formulas: triangle A=(1/2)bh, rectangle A=lw, rectangular prism V=lwh, pyramid V=(1/3)Bh (B=base area), triangular prism V=((1/2)bh)×length (triangle base area times prism length). The toy block consists of two rectangular prisms: Prism 1 volume = 6 × 4 × 2 = 48 cm³, Prism 2 volume = 3 × 4 × 2 = 24 cm³, so total volume = 48 + 24 = 72 cm³. The correct total volume is 72 cm³. Common errors include arithmetic mistakes in calculating individual volumes or in the final addition, or misunderstanding that the volumes should be added (not multiplied). Steps: (1) identify composite structure (two rectangular prisms), (2) calculate Prism 1 volume (6 × 4 × 2 = 48), (3) calculate Prism 2 volume (3 × 4 × 2 = 24), (4) add volumes since they don't overlap (48 + 24 = 72), (5) verify units (cm³). When prisms are stacked without overlap, their volumes simply add together.
A right triangular prism has a triangular base with legs 3 cm and 8 cm. The length of the prism is 7 cm. What is the volume of the prism?
Explanation: Tests solving area, volume, and surface area problems for composite figures by decomposing into simpler shapes (rectangles, triangles, prisms, pyramids), applying formulas, and combining results. Composite figures: decompose into standard shapes (L-shape as two rectangles: 10×5=50 and 6×3=18, sum: 68; or as large minus cutout: 10×8=80 minus 4×3=12, difference: 68, equivalent). Formulas: triangle A=(1/2)bh, rectangle A=lw, rectangular prism V=lwh, pyramid V=(1/3)Bh (B=base area), triangular prism V=((1/2)bh)×length (triangle base area times prism length). For this right triangular prism, the triangular base area is A=(1/2)×3×8=12 cm² (using legs as base and height), then volume is V=12×7=84 cm³. Common error would be forgetting the (1/2) factor, using 3×8=24 for base area, giving volume 168 cm³. Steps: (1) identify shape (right triangular prism), (2) calculate triangular base area using A=(1/2)×leg₁×leg₂=(1/2)×3×8=12 cm², (3) multiply by prism length for volume V=12×7=84 cm³, (4) verify units (volume in cm³). For right triangular prisms, the legs of the right triangle serve as base and height in the area formula.
A poster is shaped like a 10 in×7 in rectangle with a 3 in×4 in rectangle cut out of one corner for a logo space. What is the area of the poster that remains?
Explanation: This question tests solving area, volume, and surface area problems for composite figures by decomposing into simpler shapes (rectangles, triangles, prisms, pyramids), applying formulas, and combining results. Composite figures: decompose into standard shapes (L-shape as two rectangles: 10×5=50 and 6×3=18, sum: 68; or as large minus cutout: 10×8=80 minus 4×3=12, difference: 68, equivalent). Formulas: triangle A=(1/2)bh, rectangle A=lw, rectangular prism V=lwh, pyramid V=(1/3)Bh (B=base area), triangular prism V=((1/2)bh)×length (triangle base area times prism length). Surface area: sum all face areas (rectangular prism 3×4×5 has faces: two 3×4=12, two 3×5=15, two 4×5=20, total: 2(12+15+20)=94). For this poster, large rectangle 10 in ×7 in=70 in² minus cutout 3 in ×4 in=12 in², remaining 58 in². Common errors include adding cutout (70+12=82 in²), or wrong area (10×7=70, but cutout 3×4=12; mistake like 10×4=40). Steps: (1) identify composite structure (rectangle with cutout), (2) decompose into standard shapes (large minus small rectangle), (3) calculate each component (apply A=lw), (4) combine (subtract), (5) verify units (area in²). Decomposition choice: large-minus-small (valid).
A science class builds a triangular prism. The triangular base has base 6 cm and height 4 cm, and the prism length is 10 cm. What is the volume of the triangular prism?
Explanation: This problem tests solving volume problems for composite figures by decomposing into simpler shapes (rectangles, triangles, prisms, pyramids), applying formulas, and combining results. Formulas: triangle A=(1/2)bh, rectangle A=lw, rectangular prism V=lwh, pyramid V=(1/3)Bh (B=base area), triangular prism V=((1/2)bh)×length (triangle base area times prism length). For a triangular prism, first find the triangular base area: A = (1/2) × base × height = (1/2) × 6 × 4 = 12 cm², then multiply by prism length: V = 12 × 10 = 120 cm³. The correct volume is 120 cm³. Common errors include forgetting the (1/2) in the triangle area formula (using 6 × 4 = 24 instead of 12), which would give volume 240 cm³, or confusing dimensions. Steps: (1) identify the shape (triangular prism), (2) calculate triangular base area using A = (1/2)bh = (1/2) × 6 × 4 = 12 cm², (3) multiply base area by prism length: V = 12 × 10 = 120 cm³, (4) verify units (cm³). The key is remembering that triangular prism volume = (triangular base area) × length, and the triangular area needs the (1/2) factor.
An L-shaped classroom floor needs new carpet. The floor can be seen as a large rectangle 10 m×8 m with a rectangular corner cut out that is 4 m×3 m. What is the area of the L-shaped floor?
Explanation: Tests solving area, volume, and surface area problems for composite figures by decomposing into simpler shapes (rectangles, triangles, prisms, pyramids), applying formulas, and combining results. Composite figures: decompose into standard shapes (L-shape as two rectangles: 10×5=50 and 6×3=18, sum: 68; or as large minus cutout: 10×8=80 minus 4×3=12, difference: 68, equivalent). For this L-shaped floor, we can use the large-minus-cutout method: total rectangle area is 10×8=80 m², cutout area is 4×3=12 m², so L-shape area is 80-12=68 m². Alternatively, decompose into two rectangles: one 10×5=50 m² and one 6×3=18 m², giving 50+18=68 m² (both methods yield the same result, confirming our answer). Common error would be just using the large rectangle area (80 m²) without subtracting the cutout, or incorrect decomposition leading to wrong dimensions. Steps: (1) identify composite structure (L-shape from rectangle with corner cutout), (2) decompose (large rectangle minus small rectangle), (3) calculate each component (10×8=80, 4×3=12), (4) combine (80-12=68), (5) verify units (area in m²). The answer 68 m² correctly accounts for the cutout, while 80 m² ignores it, 92 m² adds instead of subtracts, and 56 m² likely has calculation errors.
A rectangular prism has dimensions 3 in x 4 in x 5 in. What is its total surface area?
Explanation: A rectangular prism with dimensions 3 in by 4 in by 5 in has three pairs of matching faces: two faces that are 3 by 4, two faces that are 3 by 5, and two faces that are 4 by 5. Their areas are 12, 15, and 20 square inches, and adding these together and doubling gives 2 times the sum of 12, 15, and 20, which equals 94 square inches, matching Choice A. Choice B, 60 in squared, is actually the volume of the prism, found by multiplying 3 times 4 times 5, not the surface area. Choice C, 47 in squared, is only half of the correct surface area, as if the doubling step was skipped. Choice D, 120 in squared, does not match any correct calculation for this prism.
A storage container is made by attaching two rectangular prisms side-by-side (no overlap). Prism 1 is 7 ft×3 ft×2 ft and Prism 2 is 4 ft×3 ft×2 ft. What is the total volume of the container?
Explanation: This question tests solving area, volume, and surface area problems for composite figures by decomposing into simpler shapes (rectangles, triangles, prisms, pyramids), applying formulas, and combining results. Composite figures: decompose into standard shapes (L-shape as two rectangles: 10×5=50 and 6×3=18, sum: 68; or as large minus cutout: 10×8=80 minus 4×3=12, difference: 68, equivalent). Formulas: triangle A=(1/2)bh, rectangle A=lw, rectangular prism V=lwh, pyramid V=(1/3)Bh (B=base area), triangular prism V=((1/2)bh)×length (triangle base area times prism length). Surface area: sum all face areas (rectangular prism 3×4×5 has faces: two 3×4=12, two 3×5=15, two 4×5=20, total: 2(12+15+20)=94). For this container, decompose into two prisms: 7 ft ×3 ft ×2 ft=42 ft³ and 4 ft ×3 ft ×2 ft=24 ft³, total 66 ft³ (no overlap). Common errors include adding dimensions instead of volumes (7+4=11 ×3×2=66, coincidental), or wrong volume (7×3×2=42, 4×3×2=24, but sum 60 if arithmetic error). Steps: (1) identify composite structure (two attached prisms), (2) decompose into standard shapes (two prisms), (3) calculate each component (apply V=lwh), (4) combine (add volumes), (5) verify units (volume ft³). Mistakes: double-counting overlapping areas (but none here), arithmetic errors.
A composite solid is made by stacking a smaller rectangular prism on top of a larger one. The larger prism is 9 m×5 m×2 m. The smaller prism is 4 m×5 m×3 m. What is the total volume of the composite solid?
Explanation: Tests solving area, volume, and surface area problems for composite figures by decomposing into simpler shapes (rectangles, triangles, prisms, pyramids), applying formulas, and combining results. Composite figures: decompose into standard shapes (L-shape as two rectangles: 10×5=50 and 6×3=18, sum: 68; or as large minus cutout: 10×8=80 minus 4×3=12, difference: 68, equivalent). For this composite solid with stacked prisms, calculate volumes separately: larger prism volume is 9×5×2=90 m³, smaller prism volume is 4×5×3=60 m³, so total volume is 90+60=150 m³. The prisms are stacked without overlap, so we simply add their volumes. Common error would be multiplying dimensions incorrectly or confusing which dimensions belong to which prism. Steps: (1) identify composite structure (two rectangular prisms stacked), (2) note stacking means no overlap, (3) calculate each volume (larger: 9×5×2=90, smaller: 4×5×3=60), (4) combine by addition (90+60=150), (5) verify units (volume in m³). When prisms are stacked, their volumes add directly without any subtraction.
A small park is shaped like a rectangle with two identical right triangles attached on the left and right sides. The rectangle is 6 m long and 4 m wide. Each triangle has base 4 m (the same as the rectangle’s width) and height 3 m. What is the total area of the park?
Explanation: Tests solving area, volume, and surface area problems for composite figures by decomposing into simpler shapes (rectangles, triangles, prisms, pyramids), applying formulas, and combining results. Composite figures: decompose into standard shapes (L-shape as two rectangles: 10×5=50 and 6×3=18, sum: 68; or as large minus cutout: 10×8=80 minus 4×3=12, difference: 68, equivalent). For this park, calculate rectangle area: A=6×4=24 m², then each triangle area: A=(1/2)×4×3=6 m², and since there are two identical triangles, total triangle area is 2×6=12 m², giving total park area 24+12=36 m². Common error would be forgetting the (1/2) in triangle formula (using 4×3=12 for each triangle, giving total 24+24=48) or counting only one triangle. Steps: (1) identify composite structure (rectangle with two triangles on sides), (2) decompose into shapes (one 6×4 rectangle, two 4×3 right triangles), (3) calculate each (rectangle: 6×4=24, each triangle: (1/2)×4×3=6), (4) combine (24+2×6=24+12=36), (5) verify units (area in m²). The key is remembering both the (1/2) factor for triangles and that there are two triangles to add.
A science class builds a triangular prism model. The triangular base has base 6 in and height 4 in. The length of the prism is 10 in. What is the volume of the triangular prism?
Explanation: This question tests solving volume problems for prisms by applying formulas to the base and length. For a triangular prism, decompose by finding the triangular base area A = (1/2)bh, then V = base area × length; example: triangle with b=6 in, h=4 in (area 12 in²), length 10 in, volume 120 in³. Formulas include triangle A = (1/2)bh and prism V = base area × length. For example, base (1/2)×6×4=12, times 10=120; or another prism with base 12 in² and length 10 in giving 120 in³. The correct calculation is base area (1/2)×6×4=12 in², volume 12×10=120 in³. Common errors include forgetting (1/2) for triangle (using 24 in², volume 240 in³), using wrong dimensions, or arithmetic errors (12×5=60). Steps: (1) identify the prism and base triangle, (2) calculate base area with (1/2)bh, (3) multiply by length, (4) verify units in in³. Mistakes: missing the half in triangle area, confusing area with volume units, or double-counting.
A tent stake is shaped like a triangular prism. The triangular base has base 6 cm and height 4 cm, and the prism length is 10 cm. What is the volume of the tent stake?
Explanation: This question tests solving area, volume, and surface area problems for composite figures by decomposing into simpler shapes (rectangles, triangles, prisms, pyramids), applying formulas, and combining results. Composite figures: decompose into standard shapes (L-shape as two rectangles: 10×5=50 and 6×3=18, sum: 68; or as large minus cutout: 10×8=80 minus 4×3=12, difference: 68, equivalent). Formulas: triangle A=(1/2)bh, rectangle A=lw, rectangular prism V=lwh, pyramid V=(1/3)Bh (B=base area), triangular prism V=((1/2)bh)×length (triangle base area times prism length). Surface area: sum all face areas (rectangular prism 3×4×5 has faces: two 3×4=12, two 3×5=15, two 4×5=20, total: 2(12+15+20)=94). For this triangular prism, base area (1/2)×6 cm×4 cm=12 cm², then volume 12 cm² ×10 cm=120 cm³. Common errors include missing (1/2) for triangle (using 24 cm² ×10=240 cm³), or treating as rectangular prism (6×4×10=240 cm³). Steps: (1) identify composite structure (triangular prism), (2) decompose into base triangle and length, (3) calculate each component (apply formulas: A=(1/2)bh, V=base area × length), (4) combine (multiply), (5) verify units (volume cm³). Mistakes: forgetting factors (1/2 in formula), arithmetic errors, units wrong.
A badge design is a rectangle with a triangle attached on top. The rectangle is 8 cm wide and 5 cm tall. The triangle has the same base as the rectangle (8 cm) and a height of 3 cm. What is the total area of the badge?
Explanation: This question tests solving area, volume, and surface area problems for composite figures by decomposing into simpler shapes (rectangles, triangles, prisms, pyramids), applying formulas, and combining results. Composite figures: decompose into standard shapes (L-shape as two rectangles: 10×5=50 and 6×3=18, sum: 68; or as large minus cutout: 10×8=80 minus 4×3=12, difference: 68, equivalent). Formulas: triangle A=(1/2)bh, rectangle A=lw, rectangular prism V=lwh, pyramid V=(1/3)Bh (B=base area), triangular prism V=((1/2)bh)×length (triangle base area times prism length). Surface area: sum all face areas (rectangular prism 3×4×5 has faces: two 3×4=12, two 3×5=15, two 4×5=20, total: 2(12+15+20)=94). For this badge, decompose into rectangle 8 cm ×5 cm=40 cm² and triangle (1/2)×8 cm×3 cm=12 cm², total 52 cm². Common errors include missing (1/2) for triangle (using 24 cm², total 64 cm²), or wrong base (using height as base). Steps: (1) identify composite structure (rectangle with triangle top), (2) decompose into standard shapes (rectangle and triangle), (3) calculate each component (apply A=lw, A=(1/2)bh), (4) combine (add areas), (5) verify units (area cm²). Mistakes: forgetting factors (1/2 in formula), wrong decomposition.
A garden is shaped like an L. You can decompose it into two rectangles: one rectangle is 9 m×4 m and the other is 5 m×3 m. What is the total area of the garden?
Explanation: This question tests solving area, volume, and surface area problems for composite figures by decomposing into simpler shapes (rectangles, triangles, prisms, pyramids), applying formulas, and combining results. Composite figures: decompose into standard shapes (L-shape as two rectangles: 10×5=50 and 6×3=18, sum: 68; or as large minus cutout: 10×8=80 minus 4×3=12, difference: 68, equivalent). Formulas: triangle A=(1/2)bh, rectangle A=lw, rectangular prism V=lwh, pyramid V=(1/3)Bh (B=base area), triangular prism V=((1/2)bh)×length (triangle base area times prism length). Surface area: sum all face areas (rectangular prism 3×4×5 has faces: two 3×4=12, two 3×5=15, two 4×5=20, total: 2(12+15+20)=94). For this L-shaped garden, decompose into two rectangles: 9 m ×4 m=36 m² and 5 m ×3 m=15 m², total 51 m². Common errors include multiplying dimensions wrong (9×4=36, but 5×3=15, sum 51; mistake like 9×5=45 total), or assuming overlap and subtracting. Steps: (1) identify composite structure (L-shape), (2) decompose into standard shapes (two rectangles), (3) calculate each component (apply A=lw), (4) combine (add areas), (5) verify units (area m²). Decomposition choice: two rectangles (valid, no overlap assumed).