Question

In the below figure, O is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm.
BC is joined. Find the area of the shaded region. (Take π = 3.14)

Answer 1

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Answer 2

Answer:

36.3325 cm²

Step-by-step explanation:

Given that triangle ABC is a right angled triangle we can get length BC.

We will use pythagorean theorem.

AB = the hypotenuse

AC = The height

BC = is the base of the triangle.

By pythagorean theorem :

BC² = AB² - AC²

Doing the substitution we have :

BC² = 13² - 12²

BC² = 25

BC= square root of 25 = 5 cm

Area of the shaded region = Area of semi circle - area of the triangle

Area of the triangle = ½ × base × height

= ½ × 5 × 12 = 30 cm²

Area of the semicircle = ½ × 3.14 × r²

r = 13/2 = 6.5 cm

Area of the semicircle = ½ × 3.14 × 6.5² = 66.3325 cm²

The area of the shaded region = 66.3325 cm² - 30 cm² = 36.3325 cm²

= 36.3325 cm²