Area of the square inscribed in the semicircle.
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