# Area of the square inscribed in the semicircle.

If the area of a square inscribed in a circle is 15 cm^{2} , then the area (in cm^{2}) of the square inscribed in the semicircle of the same circle is

- 6
- 5
- 3.75
- 7.5

Answer : **6**

Let pqrs be the square in full circle with sides a.

given area = a^2 = 15 cm^2

Then, sq= diameter=2*radius

a^2 + a^2 = (2*radius)^2

2a^2 = 4 * radius^2

a^2 = 2 *radius^2

radius^2 = 15/2 ——- **(i)**

Let pqrs be the square in half circle. with side x.

If we produce a mirror image of the semicircle then we get a circle and a rectangle inscribed in it.

Length of rect = 2x and Breadth of rect. = x.

Diagonal= Diameter = 2*radius

Now, (2x)^2 + x^2 = (2*radius)^2

4x^2+x^2 = 4*radius^2

5x^2 = 4*radius^2

x^2 = (4*radius^2 )/5

x^2 = (4*15/2)/5 ** [from equation i]**

x^2 = **6 **

Hence area of square in semicircle =** 6 cm^2**