Question

width 16
semi circle 1 is 10 Find the Area of the figure below, composed of a rectangle with two semicircles removed. Round to the nearest tenths place.
10
16
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Answer
Attempt 1 out of 2

Answer 1

To find the area of the figure composed of a rectangle with two semicircles removed, we need to first find the area of the rectangle and then subtract the area of the semicircles.

1. **Calculate the area of the rectangle**:
- The dimensions of the rectangle are given as width \(16\) (which is the total width of the rectangle, including where the semicircles sit).
- The height of the rectangle is \(10\).
- The area \(A_{rectangle}\) is given by:
\[
A_{rectangle} = \text{width} \times \text{height} = 16 \times 10 = 160
\]

2. **Calculate the area of the semicircles**:
- The radius of each semicircle is \(10 / 2 = 5\) because the diameter is given as \(10\).
- The area of a full circle with radius \(5\) is:
\[
A_{circle} = \pi r^2 = \pi (5^2) = 25\pi
\]
- Since each semicircle is half of a full circle, the area of one semicircle is:
\[
A_{semicircle} = \frac{1}{2} \times 25\pi = 12.5\pi
\]
- There are two semicircles, so the total area of the two semicircles is:
\[
A_{2 \, semicircles} = 2 \times 12.5\pi = 25\pi
\]

3. **Calculate the remaining area**:
- Now we subtract the area of the two semicircles from the area of the rectangle:
\[
A_{remaining} = A_{rectangle} - A_{2 \, semicircles} = 160 - 25\pi
\]

4. **Substituting \(\pi \approx 3.14\)**:
\[
25\pi \approx 25 \times 3.14 = 78.5
\]
\[
A_{remaining} \approx 160 - 78.5 = 81.5
\]

5. **Rounding to the nearest tenths place**:
The area of the figure is approximately \(81.5\).

So, the final answer is:
\[
\boxed{81.5}
\]