Unit 3 lesson 5 areas of composite figures practice answers
1) A composite figure is composed of a rectangle and a triangle. The length of the rectangle is 10 cm and its width is 6 cm. The base of the triangle is also 10 cm and its height is 3 cm. What is the area of the composite figure?
Area of the rectangle = length × width = 10 × 6 = 60 cm²
Area of the triangle = (1/2) × base × height = (1/2) × 10 × 3 = 15 cm²
Area of the composite figure = Area of the rectangle + Area of the triangle = 60 + 15 = 75 cm²
Answer: The area of the composite figure is 75 cm².
2) A composite figure is composed of two squares. The side lengths of the smaller square are 3 cm^2 and those of the larger square are 7 cm^2. What is the area of the composite figure?
Area of the smaller square = side × side = 3 × 3 = 9 cm²
Area of the larger square = side × side = 7 × 7 = 49 cm²
Area of the composite figure = Area of the smaller square + Area of the larger square = 9 + 49 = 58 cm²
Answer: The area of the composite figure is 58 cm².
3) A composite figure is composed of a rectangular garden and a semicircle on top of one side. The dimensions of the garden are 12 meters long and 7 meters wide. The diameter of the semicircle is equal to the width of the garden. What is the total area of the garden and the semicircle?
Area of the rectangular part = length × width = 12 × 7 = 84 m²
Area of the semicircle = (1/2) × π × (diameter / 2)² = (1/2) × π × (7 / 2)² = (1/2) × π × (49 / 4) ≈ 19.125 m²
Area of the composite figure = Area of the rectangular part + Area of the semicircle = 84 + 19.125 ≈ 103.125 m²
Answer: The area of the composite figure is approximately 103.125 m².