Question

Find the Area of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place.
4
16
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Answer
Attempt 2 out of 2

Answer 1

To find the area of the figure composed of a rectangle and a semicircle, we first need to determine the dimensions of both shapes.

Based on the numbers given (4 and 16), let's assume:
- The height of the rectangle is **4** units.
- The width of the rectangle is **16** units.

**Step 1: Calculate the area of the rectangle.**
The area \(A_{rectangle}\) of a rectangle is calculated using the formula:
\[
A_{rectangle} = \text{width} \times \text{height}
\]
Substituting the values:
\[
A_{rectangle} = 16 \times 4 = 64 \text{ square units}
\]

**Step 2: Calculate the area of the semicircle.**
To find the area of the semicircle, we need the radius. Since the semicircle is likely sitting on top of the rectangle, we assume the diameter of the semicircle is equal to the width of the rectangle (16 units), hence the radius \(r\) is:
\[
r = \frac{16}{2} = 8 \text{ units}
\]

The area \(A_{semicircle}\) of a semicircle is given by the formula:
\[
A_{semicircle} = \frac{1}{2} \pi r^2
\]
Substituting the radius:
\[
A_{semicircle} = \frac{1}{2} \pi (8^2) = \frac{1}{2} \pi \cdot 64 = 32\pi \text{ square units}
\]

**Step 3: Calculate the total area.**
The total area \(A_{total}\) of the figure is the sum of the area of the rectangle and the area of the semicircle:
\[
A_{total} = A_{rectangle} + A_{semicircle}
\]
Substituting the values:
\[
A_{total} = 64 + 32\pi
\]

**Step 4: Approximate and round to the nearest tenths place.**
Using \( \pi \approx 3.14 \):
\[
A_{semicircle} \approx 32 \times 3.14 = 100.48
\]
So, the total area becomes:
\[
A_{total} \approx 64 + 100.48 = 164.48
\]
Rounding to the nearest tenths place:
\[
A_{total} \approx 164.5
\]

Therefore, the area of the figure is approximately **164.5 square units**.