### A square of area 64 cm2 is inscribed into a semi-circle. What is the area of the semi-circle?

40π cm2

Step by Step Explanation:
1. The following figure shows the square inscribed into a semi-circle,

Let's assume, a is the length of the side of the square.
Therefore, AB = BC = CD = DA = a,
The area of the square = a2
2. According to the question, the area of the square is 64 cm2.
Therefore, a2 = 64 -----(1)
3. If we look at the figure carefully, we notice the OC is the radius of the semi-circle and 'O' is the center of the semi-circle.
Therefore, OA = OB =
 a 2

4. In right angled triangle OBC,
OC2 = OB2 + BC2[By the Pythagorean theorem.]
= (
 a 2
)2 + a2
=
 a2 4
+ a2
=
 5a2 4

=
 5 × 64 4
[From equation (1)]
=
 320 4

= 80 cm2
5. Now, the area of the semi-circle =
 π(OC)2 2

=
 π × 80 2

= 40π
6. Hence, the area of the semi-circle is 40π cm2.