Let’s solve each problem step by step.
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Problem 1: Rectangle
Given:
- Length = 8 cm
- Width = 3 cm
Perimeter of rectangle = 2 × (length + width)
= 2 × (8 + 3) = 2 × 11 =
22 cm
Area of rectangle = length × width
= 8 × 3 =
24 cm²
✔ Check: Perimeter adds all sides: 8+3+8+3 = 22 ✔️
Area: 8×3 = 24 ✔️
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Problem 2: Triangle
Given:
- Sides: 10 cm, 9 cm, 3 cm
Perimeter = sum of all sides
= 10 + 9 + 3 =
22 cm
Area of triangle = (base × height) ÷ 2
Here, base = 9 cm, height = 3 cm (since the vertical side is perpendicular to the base)
= (9 × 3) ÷ 2 = 27 ÷ 2 =
13.5 cm²
✔ Check: Perimeter: 10+9+3=22 ✔️
Area: ½×9×3=13.5 ✔️
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Problem 3: Trapezoid
Given:
- Parallel sides: 30 cm and 56 cm
- Height = 12 cm
- Non-parallel sides: 16 cm and 18 cm
Perimeter = sum of all sides
= 30 + 56 + 16 + 18 = let’s add:
30 + 56 = 86
16 + 18 = 34
86 + 34 =
120 cm
Area of trapezoid = (sum of parallel sides ÷ 2) × height
= ((30 + 56) ÷ 2) × 12
= (86 ÷ 2) × 12 = 43 × 12
Let’s compute: 40×12 = 480, 3×12=36 → 480+36 =
516 cm²
✔ Check: Perimeter: 30+56+16+18=120 ✔️
Area: ½×(30+56)×12 = 43×12=516 ✔️
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Problem 4: Circle
Given:
- Radius r = 3 cm
Circumference = 2 × π × r
Using π ≈ 3.14
= 2 × 3.14 × 3 = 6.28 × 3 =
18.84 cm
Area = π × r²
= 3.14 × 3² = 3.14 × 9 =
28.26 cm²
✔ Check: Circumference: 2×3.14×3=18.84 ✔️
Area: 3.14×9=28.26 ✔️
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Problem 5: Parallelogram
Given:
- Base = 6 cm
- Side = 4 cm
- Height = 3 cm
Perimeter = 2 × (base + side)
= 2 × (6 + 4) = 2 × 10 =
20 cm
Area = base × height
= 6 × 3 =
18 cm²
✔ Check: Perimeter: 6+4+6+4=20 ✔️
Area: 6×3=18 ✔️
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Final Answer:
1) Perimeter: 22 cm, Area: 24 cm²
2) Perimeter: 22 cm, Area: 13.5 cm²
3) Perimeter: 120 cm, Area: 516 cm²
4) Circumference: 18.84 cm, Area: 28.26 cm²
5) Perimeter: 20 cm, Area: 18 cm²
Parent Tip: Review the logic above to help your child master the concept of circumference and area worksheet 1.
