Let’s solve each problem one by one. We’ll find the area of each shape using the correct formula. If part is shaded, we subtract the unshaded part from the total.
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1. Square with a smaller square cut out (shaded = outer minus inner)
Outer square: 7 m × 7 m = 49 m²
Inner square: 3 m × 3 m = 9 m²
Shaded area = 49 - 9 =
40 m²
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2. Rectangle with small rectangles cut out at corners (shaded = whole rectangle minus 4 corners)
Whole rectangle: 6 ft × 12 ft = 72 ft²
Each corner is 1 ft × 1 ft → 4 corners = 4 × 1 = 4 ft²
Shaded area = 72 - 4 =
68 ft²
*(Note: The diagram shows 1-ft squares cut from each corner — standard interpretation for such problems.)*
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3. Right triangle
Base = 8 ft, Height = 6 ft
Area = (base × height) ÷ 2 = (8 × 6) ÷ 2 = 48 ÷ 2 =
24 ft²
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4. Circle with diameter 12 m → radius = 6 m
Area = π × r² = 3.14 × 6² = 3.14 × 36 =
113.04 m²
*(We use 3.14 for π unless told otherwise.)*
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5. Parallelogram
Base = 10 ft, Height = 4 ft
Area = base × height = 10 × 4 =
40 ft²
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6. Trapezoid
Bases: 3 km and 5 km, Height = 2 km
Area = [(base1 + base2) × height] ÷ 2 = [(3 + 5) × 2] ÷ 2 = (8 × 2) ÷ 2 = 16 ÷ 2 =
8 km²
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7. Triangle (right triangle)
Base = 10 cm, Height = 7 cm
Area = (10 × 7) ÷ 2 = 70 ÷ 2 =
35 cm²
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8. Circle with radius 10 ft
Area = π × r² = 3.14 × 10² = 3.14 × 100 =
314 ft²
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9. Circle with diameter 7 yd → radius = 3.5 yd
Area = π × r² = 3.14 × (3.5)² = 3.14 × 12.25 =
38.465 yd²
*(You can round to 38.5 if needed, but we’ll keep it as 38.465 for accuracy.)*
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10. Trapezoid (shaded region)
Parallel sides: 6 ft and 7 ft, Height = 6 ft
Area = [(6 + 7) × 6] ÷ 2 = (13 × 6) ÷ 2 = 78 ÷ 2 =
39 ft²
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11. Triangle
Base = 16 m, Height = 20 m
Area = (16 × 20) ÷ 2 = 320 ÷ 2 =
160 m²
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12. Parallelogram
Base = 12 ft, Height = 4 ft
Area = base × height = 12 × 4 =
48 ft²
*(The side labeled 10 ft is not needed — only base and perpendicular height matter.)*
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Final Answer:
1. 40 m²
2. 68 ft²
3. 24 ft²
4. 113.04 m²
5. 40 ft²
6. 8 km²
7. 35 cm²
8. 314 ft²
9. 38.465 yd²
10. 39 ft²
11. 160 m²
12. 48 ft²
Parent Tip: Review the logic above to help your child master the concept of area of shapes worksheet.
