Question

Find the area of the shaded region​

Answer 1

Answer:

Area of shaded region = area of trapezium -( area of circle + area of rectangle )

Answer 2

$\sf\Large{\underline{\underline{Answer:-}}}$

Given,

• A trapezium.
• Circle of diameter 7cm
• A Rectangle of dimensions 10 by 3cm.

⠀

Now, to find the Shaded portion, find the area of all the figures.

First,

• Area of trapezium

Formula using here,

${\sf { \green{ \boxed{ \sf area = {\frac{1}{2}} \times (sum \: of \: parallel \: sides) \times \: height }}}}$

Where,

• Measure of parallel sides = 25cm and 15cm
• Height (perpendicular distance) = 16cm

On substituting the Values,

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{\dfrac{1}{2} \times (25 + 15)\:}} \times 16\end{gathered}$

$\: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{\dfrac{1}{2} \times 40\:}} \times 16\end{gathered}$

$\Longrightarrow$Cancel 40 by 2, we get

$\: \: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{20\:}} \times 16\end{gathered}$

$\: \: \: \: \: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{320cm ^{2} }}\end{gathered}$

∴The area of whole figure (trapezium) is 320cm².

⠀

Now,

• Area of circle, whose diameter (d) is 7cm

Formula using here,

${\sf{\green{\boxed{\sf area = \pi \: r ^{2} }}}}$

Where,

• Radius = diameter ÷ 2 = 7 ÷ 2 = 3.5cm.

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{\frac{22}{7} \times (3.5)^{2} }}\end{gathered}$

$\: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{\frac{22}{7} \times12.25}}\end{gathered}$

$\Longrightarrow$Dividing 12.25 by 7 we get,

$\: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{\frac{22}{1} \times1.75}}\end{gathered}$

$\Longrightarrow$Now, multiply them

$\: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{38.5cm ^{2} }}}\end{gathered}$

∴ the area of circle is 38.5cm².

⠀

Now,

• Area of rectangle, whose dimensions are 3 ×10.

Formula using here,

${\sf{\green{\boxed{\sf area = length \times breadth}}}}$

Substitute the Values,

$\: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{10 \times 3}}}\end{gathered}$

$\: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{30cm^{2} }}}\end{gathered}$

∴Area of rectangle is 30cm².

⠀

Now,

To find the Shaded portion subtract the area internal figures from the trapezium,

• Shaded portion = Area of trapezium - (area of Circle + area of Rectangle)

Shaded portion = 320cm² - (38.5cm² + 30cm²)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 320cm² – 68.5cm²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 251.5cm²

$\sf\underbrace{Hence,}$

The area of shaded portion is 251.5cm².