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.

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.

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).

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).

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.

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.

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).

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.

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.

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: $10 \times 5 = 50$ and $6 \times 3 = 18$, sum: 68; or as large minus cutout: $10 \times 8 = 80$ minus $4 \times 3 = 12$, difference: 68, equivalent). Surface area: sum all face areas (rectangular prism 3×4×5 has faces: two $3 \times 4 = 12$, two $3 \times 5 = 15$, two $4 \times 5 = 20$, total: $2(12+15+20)=94$). For this 3×4×5 prism, calculate areas of three pairs of faces: two $3 \times 4 = 12$ in² faces, two $3 \times 5 = 15$ in² faces, two $4 \times 5 = 20$ in² faces, giving total surface area $2(12+15+20)=2(47)=94$ in². Common error would be calculating volume ($3 \times 4 \times 5 = 60$) instead of surface area, or missing faces/counting wrong. Steps: (1) identify all 6 faces of rectangular prism, (2) group into 3 pairs of identical opposite faces, (3) calculate area of each type ($3 \times 4 = 12$, $3 \times 5 = 15$, $4 \times 5 = 20$), (4) sum with factor of 2 for pairs: $2(12+15+20)=94$, (5) verify units (surface area in in²). Surface area requires summing all face areas, not multiplying dimensions like volume.