Area of Composite Figures Practice
1. Find the area of the following composite figure:
- The figure consists of a square with side length 6 cm and a semicircle on top of the square.
Solution:
- Area of the square = side length x side length = 6 cm x 6 cm = 36 sq cm
- Area of the semicircle = 1/2 x π x radius^2 = 1/2 x π x (6/2)^2 = 1/2 x π x 3^2 = 4.5π sq cm
- Total area = area of square + area of semicircle = 36 sq cm + 4.5π sq cm ≈ 36 + 14.13 ≈ 50.13 sq cm
2. Find the area of the following composite figure:
- The figure consists of a rectangle with length 8 cm and width 5 cm, and a triangle on top of the rectangle with base 8 cm and height 4 cm.
Solution:
- Area of the rectangle = length x width = 8 cm x 5 cm = 40 sq cm
- Area of the triangle = 1/2 x base x height = 1/2 x 8 cm x 4 cm = 16 sq cm
- Total area = area of rectangle + area of triangle = 40 sq cm + 16 sq cm = 56 sq cm
3. Find the area of the following composite figure:
- The figure consists of a triangle with base 12 cm and height 8 cm, and a semicircle on top of the triangle with radius 6 cm.
Solution:
- Area of the triangle = 1/2 x base x height = 1/2 x 12 cm x 8 cm = 48 sq cm
- Area of the semicircle = 1/2 x π x radius^2 = 1/2 x π x 6 cm x 6 cm = 18π sq cm
- Total area = area of triangle + area of semicircle = 48 sq cm + 18π sq cm ≈ 48 + 56.55 ≈ 104.55 sq cm
4. Find the area of the following composite figure:
- The figure consists of a rectangle with length 10 cm and width 6 cm, and a quarter circle on the top right corner of the rectangle with radius 4 cm.
Solution:
- Area of the rectangle = length x width = 10 cm x 6 cm = 60 sq cm
- Area of the quarter circle = 1/4 x π x radius^2 = 1/4 x π x 4 cm x 4 cm = 4π sq cm
- Total area = area of rectangle + area of quarter circle = 60 sq cm + 4π sq cm ≈ 60 + 12.57 ≈ 72.57 sq cm