Question

find the area of the given figure. 6 m 12 m 18.1 m² 72 m² 57.9 m² 86.1 m²

Explanation:

Step1: Calculate area of rectangle

The rectangle has length \( 12 \, \text{m} \) and width \( 6 \, \text{m} \). The formula for the area of a rectangle is \( A_{\text{rectangle}} = \text{length} \times \text{width} \).
\[
A_{\text{rectangle}} = 12 \times 6 = 72 \, \text{m}^2
\]

Step2: Calculate area of semicircle

The diameter of the semicircle is \( 6 \, \text{m} \), so the radius \( r = \frac{6}{2} = 3 \, \text{m} \). The formula for the area of a full circle is \( A_{\text{circle}} = \pi r^2 \), so the area of a semicircle is \( A_{\text{semicircle}} = \frac{1}{2} \pi r^2 \). Using \( \pi \approx 3.14 \):
\[
A_{\text{semicircle}} = \frac{1}{2} \times 3.14 \times 3^2 = \frac{1}{2} \times 3.14 \times 9 = 14.13 \, \text{m}^2
\]

Step3: Calculate total area

Add the area of the rectangle and the area of the semicircle:
\[
A_{\text{total}} = A_{\text{rectangle}} + A_{\text{semicircle}} = 72 + 14.13 = 86.13 \approx 86.1 \, \text{m}^2
\]

Answer:

\( 86.1 \, \text{m}^2 \) (the option with \( 86.1 \, \text{m}^2 \))