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Q.

[[1]] the area of the shaded region in figure, if PQ=24cm, PR=7cm and O is the centre of the circle.

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Detailed Solution

Given data:
The length of the circular arc of radius = 6 cm.
Each side of the equilateral triangle is 12cm.
From the figure we get,
The area of the shaded part = The area of the equilateral triangle + The area of the major sector
Area of the major arc is

\frac{θ}{360} ° \times π r^{2}

So, we have r = 6, θ = 300∘
=

\frac{300 °}{360 °} \times π \times 6^{2}

The area of the major arc: 94.2

{c m^{2}}^{}

.
Now the area of an equilateral triangle with each side a is 3–√4a2 sq. cm.
= 3–√4×122
The area of the equilateral triangle: 62.352

{c m^{2}}^{}

.
The area of the shaded part = The area of the equilateral triangle + The area of the major sector
= 62.352+94.2 sq. cm
=156.55

c m^{2}

Hence, the area of the shaded region is 156.55

{c m^{2}}^{}

.

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