A square of area 64 cm2 is inscribed into a semi-circle. What is the area of the semi-circle?
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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 = a2
- According to the question, the area of the square is 64 cm2.
Therefore, a2 = 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 =
- In right angled triangle OBC,
OC2 = OB2 + BC2 [By the Pythagorean theorem.]
= ( )2 + a2
= + a2
= [From equation (1)]
= 80 cm2
- Now, the area of the semi-circle =
- Hence, the area of the semi-circle is 40π cm2.