The ΔPQR is inscribed in a semicircle. PQ = PR = 7cm . Find the area of the shaded region.

# The $\Delta$PQR is inscribed in a semicircle. PQ = PR = 7cm . Find the area of the shaded region.

1. A
14
2. B
26
3. C
50
4. D
20

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### Solution:

The measure of the angle prescribed by the diameter of the semicircle on its circumference is 90°. So
∠QPR = 90°.
Therefore, $\Delta$PQR is a right-angled triangle.
Area of a right-angled triangle is,
To find the area of the semicircle, we have to find out its radius first.
As $\Delta$PQR  is a right-angled triangle, so by applying Pythagoras theorem, we get
cm
is the diameter of the semicircle, we know that radius is half of the diameter of the circle, so cm.
The area of the semicircle is                                                                 The area of the shaded region is
Hence the area of the shaded region is 14 $c{m}^{2}$.
Hence, Option (1) is the correct answer.

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