Question

a triangle is placed in a semicircle with a radius of 4 ft, as shown below. find the area of the shaded region.
use the value 3.14 for $pi$, and do not round your answer. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate area of semicircle

The formula for the area of a full circle is $\pi r^2$, so the area of a semicircle is $\frac{1}{2} \pi r^2$. Substituting $r=4$ ft and $\pi=3.14$:
$\frac{1}{2} \times 3.14 \times 4^2 = \frac{1}{2} \times 3.14 \times 16 = 25.12$ $\text{ft}^2$

Step2: Calculate area of triangle

The triangle has a base equal to the diameter of the semicircle ($2r=8$ ft) and height equal to the radius ($4$ ft). The area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$:
$\frac{1}{2} \times 8 \times 4 = 16$ $\text{ft}^2$

Step3: Find shaded area (subtract areas)

Subtract the area of the triangle from the area of the semicircle:
$25.12 - 16 = 9.12$ $\text{ft}^2$

Answer:

$9.12$ square feet