What is the area of this figure? 6 in 4 in 6 in 3 in 3 in 2 in Write your answer using decimals. Use 3.14 for
. square inches 2 in
The Correct Answer and Explanation is:
To find the area of this compound figure, we can break it down into two simpler shapes: a polygon on the right and a semicircle on the left.
1. Calculate the area of the polygon.
The polygon on the right can be divided into smaller, non-overlapping rectangles. A convenient way to do this is to split it into a top rectangle and a bottom L-shaped section.
- Top Rectangle: The dimensions are given as 6 inches (height) and 4 inches (width).
Area of top rectangle = height × width = 6 in × 4 in = 24 square inches. - Bottom L-shaped section: This part can be further divided into two rectangles.
- One way is to split it into a bottom horizontal rectangle and a smaller vertical rectangle. The bottom horizontal rectangle has a width of 6 inches and a height of 2 inches. The remaining vertical rectangle has a height of 3 inches and its width is the total width (6 in) minus the width of the indent (2 in), which is 4 inches.
- Area of bottom rectangle = 6 in × 2 in = 12 square inches.
- Area of middle rectangle = 4 in × 3 in = 12 square inches.
- Alternatively, the area of the L-shape is the sum of these two: 12 + 12 = 24 square inches.
- Total Area of the Polygon: Add the areas of the parts.
Area of polygon = Area of top rectangle + Area of L-shape = 24 sq in + 24 sq in = 48 square inches.
2. Calculate the area of the semicircle.
The curved part on the left is a semicircle attached to the straight vertical side of the polygon.
- Find the diameter: The diameter of the semicircle is equal to the total height of the polygon it is attached to. We find the total height by summing the vertical segments of the polygon: 6 in + 3 in + 2 in = 11 inches.
So, the diameter (d) of the semicircle is 11 inches. - Find the radius: The radius (r) is half of the diameter.
r = d / 2 = 11 in / 2 = 5.5 inches. - Calculate the area: The formula for the area of a semicircle is (1/2)πr². Using 3.14 for π:
Area of semicircle = (1/2) × 3.14 × (5.5)²
Area of semicircle = 0.5 × 3.14 × 30.25
Area of semicircle = 47.4925 square inches.
3. Calculate the total area of the figure.
The total area is the sum of the area of the polygon and the area of the semicircle.
- Total Area = Area of polygon + Area of semicircle
- Total Area = 48 + 47.4925
- Total Area = 95.4925 square inches.
The area of the figure is 95.4925 square inches.
