Question

The diagram below shows a semicircle with centre O. Taking n = 3.14, find

27.
the shaded area.
O
​

Answer 1

11.12 cm^2.

Explanation:

The area of the shaded part = Area of the semicircle - area of the triangle.

The base of the triangle has length 8 - 1 = 7 cm and it's height is equal to the radius of the semicircle which is 4 cm.

So our shaded area = 1/2 * 3.14 * 4^2 - 1/2 * 7 * 4

= 25.12 - 14

= 11.12 cm^2.

Answer 2

11.12 cm^2

`solution \\ area \: of \: triangle = (1)/(2) * b * h \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (1)/(2) * 7 * 4 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 14 \: {cm}^(2) \\ area \: of \: semicircle = \frac{\pi \: {r}^(2) }{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{3.14 * {4}^(2) }{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (3.14 * 16)/(2) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 25.12 \: {cm}^(2) \\ area \: of \: shaded \: region \\ = area \: of \: semicircle - area \: of \: triangle \\ = 25.12 - 14 \\ = 11.12 \: {cm}^(2)`

hope this helps...

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