Question

The diagram below shows a semicircle with centre O. Taking n = 3.14, find
27.
the shaded area.
O
​

Answer 1

Answer:

11.12 cm^2

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

hope this helps...

Good luck on your assignment...

Answer 2

Answer:

11.12 cm^2.

Step-by-step 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.