Question

find the area of the shaded segment of the circle. round your answer to two decimal places. draw

Explanation:

Step1: Calculate the area of the sector

The formula for the area of a sector is $A_{sector}=\frac{\theta}{360}\times\pi r^{2}$. Here, $\theta = 90^{\circ}$ (since it's a right - angled sector) and $r = 13\ \text{m}$.
$$A_{sector}=\frac{90}{360}\times\pi\times(13)^{2}=\frac{1}{4}\times\pi\times169 = 42.25\pi\ \text{m}^2$$

Step2: Calculate the area of the triangle

The formula for the area of a right - angled triangle is $A_{triangle}=\frac{1}{2}\times base\times height$. Here, base $= 13\ \text{m}$ and height $= 13\ \text{m}$.
$$A_{triangle}=\frac{1}{2}\times13\times13=\frac{169}{2}=84.5\ \text{m}^2$$

Step3: Calculate the area of the segment

The area of the segment $A = A_{sector}-A_{triangle}$.
$$A = 42.25\pi-84.5$$
Substitute $\pi\approx3.14159$:
$$A\approx42.25\times3.14159 - 84.5$$
$$A\approx132.89 - 84.5=36.39\ \text{m}^2$$

Answer:

$36.39\ \text{m}^2$