This question tests finding the area of a trapezoid by decomposing into a rectangle and a right triangle, using A = lw and (1/2)bh, summing to total. Strategies: rectangle 6 cm × 4 cm = 24 cm², triangle (1/2)×4 cm×4 cm = 8 cm², total 32 cm². Formulas: rectangle A = lw, triangle (1/2)bh as half rectangle; example, similar trapezoid bases 6 and 10, height 4: 24+8=32. Like triangle half 24=12, L-shape 30+12=42. The correct area is 24 + 8 = 32 cm² using decomposition. Errors include no 1/2 for triangle getting 24+16=40, or wrong base like 10×4=40. Decomposing: (1) identify parts, (2) divide, (3) calculate and sum; real-world for boards like covering. Mistakes: arithmetic like 24+8=30, forgetting squared units.

This question tests finding the area of polygons by composing into rectangles (large minus cutout) or decomposing into triangles/rectangles (sum parts), using A=(1/2)bh for triangles, A=lw for rectangles. Strategies include decomposing by breaking into simpler shapes like a triangle as half a rectangle with A=(1/2)bh, L-shape as two rectangles summing areas, or composing by enclosing in a rectangle and subtracting outside parts, such as a right triangle in a 6×4 rectangle giving (1/2)×24=12. Formulas are rectangle A=lw (length×width), triangle A=(1/2)bh (base×height divided by 2—half of a rectangle); example: trapezoid bases 6 and 10, height 4, decompose into rectangle 6×4=24 plus triangle base 4, height 4: (1/2)×4×4=8, total 32. For this patio, decompose into two rectangles: 5×6=30 m² and 3×4=12 m², summing to 42 m². A common error is adding wrong, like 30+12=40, or treating as one shape without decomposing. To decompose, identify simpler shapes like rectangles and triangles, draw dividing lines, calculate each (rectangle: lw, triangle: (1/2)bh), and sum; for composing, enclose in rectangle, identify cutouts, calculate, and subtract. Real-world: patio area for paving; mistakes include arithmetic errors or forgetting non-overlapping parts.

This question tests finding the area of a right triangle by using A = (1/2)bh, composing it as half of a rectangle. Strategies include directly applying the formula for the triangle with base 6 cm and height 4 cm, or composing a 6×4 rectangle of 24 cm² and taking half for 12 cm². Formulas: triangle A = (1/2)bh, which is half of a rectangle's A = lw with same base and height; example, trapezoid bases 6 and 10, height 4, decomposes to rectangle 24 plus triangle 8 for 32. For example, this right triangle base 6, height 4 is (1/2)×6×4=12, or half of 24=12; an L-shape might be 48 minus 6=42 by composition. The correct area is (1/2)×6×4 = 12 cm² using the formula. A common error is forgetting the 1/2, calculating bh=24 instead of 12, or mixing with rectangle formula. For triangles: always use (1/2)bh; real-world like pennant fabric area. Steps: identify base and height, multiply and halve; mistakes include arithmetic errors or unsquared units.

This question tests finding the area of polygons by composing into rectangles (large minus cutout) or decomposing into triangles/rectangles (sum parts), using A=(1/2)bh for triangles, A=lw for rectangles. Strategies: decompose (break into simpler shapes: triangle as half rectangle with A=(1/2)bh, L-shape as two rectangles summing areas), compose (enclose in rectangle, subtract outside parts: right triangle in 6×4 rectangle is (1/2)×24=12). Formulas: rectangle A=lw (length×width), triangle A=(1/2)bh (base×height divided by 2—half of rectangle). Example: trapezoid bases 6 and 10, height 4, decompose into rectangle 6×4=24 plus triangle with base 4, height 4: (1/2)×4×4=8, total 24+8=32. Example: right triangle base 6, height 4, fits in rectangle 6×4=24, triangle is half: (1/2)×24=12, or directly (1/2)×6×4=12; or L-shape: large rectangle 8×6=48 minus cutout 3×2=6 gives 48-6=42, or decompose into rectangles 5×6=30 and 3×4=12, sum 30+12=42 (both methods work). The correct area is found by decomposing: rectangle 8 ft × 5 ft = 40 ft² plus triangle (1/2) × 8 ft × 3 ft = 12 ft², total 52 ft². A common error is forgetting the 1/2 for the triangle (40 + 24 = 64 ft²), or using rectangle height for triangle base, or arithmetic like 40 + 12 = 54. Decomposing: (1) identify simpler shapes (can polygon be split into rectangles and triangles?), (2) draw lines dividing (dotted lines showing decomposition), (3) calculate each part (rectangle: lw, triangle: (1/2)bh), (4) sum (total=part₁+part₂+...). Composing: (1) enclose in rectangle (smallest rectangle containing polygon), (2) identify cutouts (triangles or rectangles outside polygon), (3) calculate rectangle and cutouts, (4) subtract (rectangle area minus cutout areas). Triangle key: A=(1/2)bh always (half of rectangle with same base and height). Real-world: room area for flooring (L-shaped room composed/decomposed), garden area for fencing, window area for glass. Mistakes: forgetting (1/2) for triangles, wrong decomposition (incorrect shapes), arithmetic errors, units not squared.

This question tests finding the area of polygons by composing into rectangles (large minus cutout) or decomposing into triangles/rectangles (sum parts), using A=(1/2)bh for triangles, A=lw for rectangles. Strategies include decomposing by breaking into simpler shapes like a triangle as half a rectangle with A=(1/2)bh, L-shape as two rectangles summing areas, or composing by enclosing in a rectangle and subtracting outside parts, such as a right triangle in a 6×4 rectangle giving (1/2)×24=12. Formulas are rectangle A=lw (length×width), triangle A=(1/2)bh (base×height divided by 2—half of a rectangle); example: trapezoid bases 6 and 10, height 4, decompose into rectangle 6×4=24 plus triangle base 4, height 4: (1/2)×4×4=8, total 32 in². The student computed (6+10)×4=64, but the correct area is (6+10)/2 ×4=32 in², forgetting to divide by 2 for the average base. A common error is halving wrong, like (6+10)×(4/2)=32 but misplaced, or arithmetic like (16/2)×4=30. To decompose, identify simpler shapes, draw lines, calculate parts, and sum; for composing, enclose in rectangle, identify cutouts, and subtract. Real-world: window area for glass; mistakes include forgetting to average bases or units not squared.

This question tests finding the area of polygons by composing into rectangles (large minus cutout) or decomposing into triangles/rectangles (sum parts), using A=(1/2)bh for triangles, A=lw for rectangles. Strategies include decomposing by breaking into simpler shapes like a triangle as half a rectangle with A=(1/2)bh, L-shape as two rectangles summing areas, or composing by enclosing in a rectangle and subtracting outside parts, such as a right triangle in a 6×4 rectangle giving (1/2)×24=12. Formulas are rectangle A=lw (length×width), triangle A=(1/2)bh (base×height divided by 2—half of a rectangle); for this trapezoid with bases 6 and 10, height 4, decompose into rectangle 6×4=24 plus triangle base 4, height 4: (1/2)×4×4=8, total 32 cm², or use average base (6+10)/2×4=32. For example, an L-shape: large rectangle 8×6=48 minus cutout 3×2=6 gives 48-6=42, or decompose into 5×6=30 and 3×4=12 summing to 42. A common error is forgetting to average the bases, like (6+10)×4=64 without dividing by 2, or arithmetic like 24+8=30 instead of 32. To decompose, identify simpler shapes, draw lines dividing, calculate each part (rectangle: lw, triangle: (1/2)bh), and sum; for composing, enclose in rectangle, identify cutouts, calculate, and subtract. Triangle key: A=(1/2)bh always; real-world: table top area for covering, mistakes include wrong decomposition or units not squared.

This question tests finding the area of polygons by composing into rectangles (large minus cutout) or decomposing into triangles/rectangles (sum parts), using A=(1/2)bh for triangles, A=lw for rectangles. Strategies include decomposing by breaking into simpler shapes like a triangle as half a rectangle with A=(1/2)bh, or composing by enclosing in a rectangle and subtracting outside parts, such as a right triangle in a 6×4 rectangle giving (1/2)×24=12. Formulas are rectangle A=lw (length×width), triangle A=(1/2)bh (base×height divided by 2—half of a rectangle); for example, a trapezoid with bases 6 and 10, height 4, can be decomposed into a rectangle 6×4=24 plus a triangle with base 4, height 4: (1/2)×4×4=8, total 24+8=32. For this right triangle with base 6 m and height 4 m, you can compose it into a 6×4 rectangle of area 24 and take half, or directly use (1/2)×6×4=12 m². A common error is treating it like a rectangle without dividing by 2, getting 6×4=24 m² instead of 12. To decompose, identify simpler shapes like triangles, draw dividing lines, calculate each part using (1/2)bh, and sum them up; for composing, enclose in a rectangle, identify cutouts, calculate areas, and subtract. Remember, a triangle's area is always (1/2)bh as it's half a rectangle with the same base and height; in real-world uses, like garden areas for planting, mistakes include forgetting the 1/2 for triangles or arithmetic errors like 6×4=26.

This question tests finding the area of polygons by composing into rectangles (large minus cutout) or decomposing into triangles/rectangles (sum parts), using A=(1/2)bh for triangles, A=lw for rectangles. Strategies: decompose (break into simpler shapes: triangle as half rectangle with A=(1/2)bh, L-shape as two rectangles summing areas), compose (enclose in rectangle, subtract outside parts: right triangle in 6×4 rectangle is (1/2)×24=12). Formulas: rectangle A=lw (length×width), triangle A=(1/2)bh (base×height divided by 2—half of rectangle). Example: trapezoid bases 6 and 10, height 4, decompose into rectangle 6×4=24 plus triangle with base 4, height 4: (1/2)×4×4=8, total 24+8=32. Example: right triangle base 6, height 4, fits in rectangle 6×4=24, triangle is half: (1/2)×24=12, or directly (1/2)×6×4=12; or L-shape: large rectangle 8×6=48 minus cutout 3×2=6 gives 48-6=42, or decompose into rectangles 5×6=30 and 3×4=12, sum 30+12=42 (both methods work). The correct area is found using the triangle formula: (1/2) × 6 ft × 4 ft = 12 ft², or by composing into a 6 ft × 4 ft rectangle (24 ft²) and taking half. A common error is forgetting the 1/2 and calculating as a rectangle (6 × 4 = 24 ft²), or mixing up base and height, or arithmetic like (1/2) × 6 × 4 = 24 instead of 12. Decomposing: (1) identify simpler shapes (can polygon be split into rectangles and triangles?), (2) draw lines dividing (dotted lines showing decomposition), (3) calculate each part (rectangle: lw, triangle: (1/2)bh), (4) sum (total=part₁+part₂+...). Composing: (1) enclose in rectangle (smallest rectangle containing polygon), (2) identify cutouts (triangles or rectangles outside polygon), (3) calculate rectangle and cutouts, (4) subtract (rectangle area minus cutout areas). Triangle key: A=(1/2)bh always (half of rectangle with same base and height). Real-world: room area for flooring (L-shaped room composed/decomposed), garden area for fencing, window area for glass. Mistakes: forgetting (1/2) for triangles, wrong decomposition (incorrect shapes), arithmetic errors, units not squared.

This question tests finding the area of a trapezoid using A = (1/2)(b1 + b2)h, which relates to decomposing into a rectangle and triangles. Strategies include using the formula directly for bases 6 ft and 10 ft, height 4 ft, giving (1/2)×16×4=32 ft², or decomposing into a rectangle and triangle. Formulas: trapezoid as average bases times height, rectangle A=lw, triangle (1/2)bh; example, this trapezoid decomposes to 6×4=24 plus (1/2)×4×4=8 for 32. Like a right triangle in 6×4=24, half is 12; or L-shape 48-6=42. The correct area is (1/2)(6+10)×4 = 32 ft² using the formula. Errors include not halving, getting 16×4=64, or adding bases wrong like 6+10=18. Decomposing: (1) split into rectangle and triangle, (2) calculate each, (3) sum; real-world for tabletops like painting area. Mistakes: forgetting 1/2 in formula, arithmetic like 8×4=36 instead of 32, squared units.

This question tests finding the area of an irregular mat by composing a large rectangle and subtracting a triangular cutout, using A = lw minus (1/2)bh. Strategies: large 12 ft × 7 ft = 84 ft², cutout (1/2)×6×3=9 ft², area 84-9=75 ft². Formulas: rectangle A = lw, triangle (1/2)bh; example, trapezoid 24 + 8 = 32. Like L-shape 48-6=42, triangle 12. The correct area is 84 - 9 = 75 ft² using composition. Errors include full triangle 18, 84-18=66, or no subtract 84. Composing: (1) enclose, (2) identify cutout, (3) calculate, (4) subtract; real-world for mats like cleaning area. Mistakes: forgetting 1/2, arithmetic like 84-9=74, unsquared units.