Let’s solve each problem one by one. We’ll use the formulas for area that you’ve learned:
- Circle: Area = π × r²
- Triangle: Area = ½ × base × height
- Trapezoid: Area = ½ × (base₁ + base₂) × height
- Parallelogram: Area = base × height
- Rectangle/Square: Area = length × width
We’re told to use π = 22/7 where needed.
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Problem 1: Circle with radius 4 ft
Area = π × r² = (22/7) × 4² = (22/7) × 16
Calculate:
22 × 16 = 352
So, 352 ÷ 7 = 50 and 2/7 →
50 2/7 ft²
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Problem 2: Trapezoid with bases 9 m and 5 m, height 3 m
Area = ½ × (9 + 5) × 3 = ½ × 14 × 3 = 7 × 3 =
21 m²
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Problem 3: Parallelogram with base 8 yd, height 4 yd
Area = base × height = 8 × 4 =
32 yd²
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Problem 4: Triangle with base 6 in, height 5 in
Area = ½ × 6 × 5 = 3 × 5 =
15 in²
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Problem 5: Rectangle with length 5/2 ft, width 4/3 ft
Area = length × width = (5/2) × (4/3) = (5×4)/(2×3) = 20/6 = 10/3 =
3 1/3 ft²
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Problem 6: Square with side 5/4 ft
Area = side × side = (5/4) × (5/4) = 25/16 =
1 9/16 ft²
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Problem 7: Height of triangle is 2/3 yards, area is 1/2 yard². Find base.
Formula: Area = ½ × base × height
Plug in what we know:
1/2 = ½ × base × (2/3)
Multiply both sides by 2 to cancel the ½ on the right:
1 = base × (2/3)
Now divide both sides by 2/3 (or multiply by reciprocal 3/2):
base = 1 × (3/2) =
3/2 yards or 1 1/2 yards
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Problem 8: Parallelogram with height 3/4 foot, base 2 feet. Find area.
Area = base × height = 2 × (3/4) = 6/4 = 3/2 =
1 1/2 ft²
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Final Answer:
1. 50 2/7 ft²
2. 21 m²
3. 32 yd²
4. 15 in²
5. 3 1/3 ft²
6. 1 9/16 ft²
7. 1 1/2 yards
8. 1 1/2 ft²
Parent Tip: Review the logic above to help your child master the concept of area mixed shapes worksheet.
