### A square of area 64 cm^{2} is inscribed into a semi-circle. What is the area of the semi-circle?

**Answer:**

40π cm^{2}

**Step by Step Explanation:**

- 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 = a^{2} - According to the question, the area of the square is 64 cm
^{2}.

Therefore, a^{2}= 64 -----(1) - 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 - In right angled triangle OBC,

OC^{2}= OB^{2}+ BC^{2}**[By the Pythagorean theorem.]**

= (

)a 2 ^{2}+ a^{2}

=

+ aa ^{2}4 ^{2}

=5a ^{2}4

=5 × 64 4 **[From equation (1)]**

=320 4

= 80 cm^{2} - Now, the area of the semi-circle =
π(OC) ^{2}2

=π × 80 2

= 40π - Hence, the area of the semi-circle is
**40π**cm^{2}.