Use the image to answer the question. What is the area of the composite figure?
To find the area of the composite figure, we need to divide it into three separate shapes: a rectangle, a triangle, and a semicircle.
1. Rectangle:
Base = 6 cm
Height = 4 cm
Area = Base x Height
Area = 6 cm x 4 cm
Area = 24 cm²
2. Triangle:
Base = 6 cm
Height = 3 cm
Area = (Base x Height) / 2
Area = (6 cm x 3 cm) / 2
Area = 9 cm²
3. Semicircle:
Radius = 2 cm
Area = πr² / 2
Area = π(2 cm)² / 2
Area = π(4 cm²) / 2
Area = 2π cm²
Now, add up the areas of the rectangle, triangle, and semicircle to find the total area of the composite figure:
Total Area = Rectangle Area + Triangle Area + Semicircle Area
Total Area = 24 cm² + 9 cm² + 2π cm²
Total Area ≈ 33.28 cm² (rounded to two decimal places)
Therefore, the area of the composite figure is approximately 33.28 cm².