Composite figures Question 1 What is the area of the composite figure to the nearest square centimeter? Responses A 21 21 cm 2 B 29 29 cm 2 C 37 37 cm 2 D 58 58 cm 2 Question 2 If half circles are added to both ends of the composite figure, what is the area of the composite figure to the nearest square centimeter? Responses A 44 44 cm 2 B 57 57 cm 2 C 65 65 cm 2 D 94 94 cm 2
Question 1: To find the area of the composite figure, we need to calculate the area of each individual shape and then add them together. The composite figure consists of a rectangle and two triangles.
Area of rectangle = length x width = 6 x 5 = 30 cm^2
Area of each triangle = 1/2 x base x height
Area of each triangle = 1/2 x 6 x 4 = 12 cm^2
Total area = 30 + 12 + 12 = 54 cm^2
Therefore, the area of the composite figure is closest to 54 cm^2.
Answer: D 58 cm^2
Question 2: Adding half circles to both ends of the composite figure will increase its area. The composite figure will now consist of a rectangle, two triangles, and two half circles.
The diameter of the half circles is the same as the width of the rectangle, which is 5 cm.
Area of each half circle = 1/2 x π x r^2 (where r is the radius)
Area of each half circle = 1/2 x π x (5/2)^2 = 1/2 x π x 6.25 = 9.82 cm^2
Total area = 54 + 9.82 + 9.82 = 73.64 cm^2
Therefore, the area of the composite figure with half circles added is closest to 74 cm^2.
Answer: D 94 cm^2