37. find the area of the shaded part in the figure shown below. (use $\pi=\frac{22}{7}$)

Question

Accepted Answer

# Explanation:
## Step1: Calculate the area of the sector
The formula for the area of a sector is $A=\frac{\theta}{360}\times\pi r^{2}$. Here, $\theta = 90^{\circ}$ (since it's a right - angled sector) and $r = 21$ in.
$$
\begin{align*}
A_{sector}&=\frac{90}{360}\times\frac{22}{7}\times21\times21\
&=\frac{1}{4}\times\frac{22}{7}\times21\times21\
&=\frac{1}{4}\times22\times3\times21\
&=\frac{1386}{2}\
& = 693\text{ in}^2
\end{align*}
$$
## Step2: Calculate the area of the right - angled triangle
The formula for the area of a right - angled triangle is $A=\frac{1}{2}\times base\times height$. Here, $base = 21$ in and $height = 21$ in.
$$
\begin{align*}
A_{triangle}&=\frac{1}{2}\times21\times21\
&=\frac{441}{2}\
&=220.5\text{ in}^2
\end{align*}
$$
## Step3: Calculate the area of the shaded region
The area of the shaded region $A = A_{sector}-A_{triangle}$
$$
\begin{align*}
A&=693 - 220.5\
&=472.5\text{ in}^2
\end{align*}
$$

# Answer:
$472.5$ square inches

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the area of the sector

Step2: Calculate the area of the right - angled triangle

Step3: Calculate the area of the shaded region

Answer: