Question

in the following figure o us the center of a semi circular are and AOB is a straight line find the area of shaded region.

Answer 1

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Answer 2

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$\Large\bold{\underline{\red{Question}}}$

The given figure shows the center of a circular arc and AOB is a straight line. Find the perimeter and the area of the shaded region correct to one decimal place. (Take π=3.142)

$\small\fbox\pink{Answer:61.1cm}$

$\Large\bold{\underline{\red{Answer}}}$

In right angle triangle ACB,

$\fbox\orange{AB ² = AC² + BC²}$

⟹ (12)² + (16)² = 144 + 256 = 400

$AB = \sqrt{400}$

∴ Diameter = 20m

Radius

$= \frac{20}{2} = 10m$

Arc length ACB

$= \frac{1}{2}×2πr$

$=\frac{1}{2}×2×3.142×10$

= $\small\fbox\blue{31.42m}$

Perimeter of shaded region

$=31.42+12+16$

= $\small\fbox\blue{59.42cm}$

Area of shaded region

$= \frac{1}{2} πr² - \frac{1}{2} ×AC×CB$

$= \frac{1}{2}(3.142×10² −12×16)$

$= \frac{1}{2} (314.2−192)$

$=\frac{1}{2} ×122.2$

= $\small\fbox\pink{61.1cm}$

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