The ΔPQR is inscribed in a semicircle. PQ = PR = 7cm . Find the area of the shaded region. - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

The measure of the angle prescribed by the diameter of the semicircle on its circumference is 90°. So
∠QPR = 90°.
Therefore,

Δ

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

Δ

PQR is a right-angled triangle, so by applying Pythagoras theorem, we get

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.

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