Question

133) OABC is a rhombus whose 3 vertices A, B, C lie on the circle with
lie on the circle with centre 0. If the
radius of the circle is 10cm, find the area of the shaded region. (T1 = 3.14, 73=1.7)​

Answer 1

Answer:

Area of shaded region=area of circle-area of rhombus

Step-by-step explanation:

$area \: of \: circle = \pi {r}^{2} \\ \: \: \: \: \: \: \: = 3.14 \times 10 \times 10 \\ \: \: \: \: \: \: \: = 314 \: c {m}^{2}$

join OB and OC

let the intersection point of diagonal OB and OC be M

OB=10 cm

We know that diagonals of rhombus bisect each other at 90 degree

so OM = 5 cm

and triangle OMC is right angled triangle.

$m{c }^{2} = o {c}^{2} - o {m}^{2} \\ \: \: \: = {10}^{2} - {5}^{2} \\ \: \: \: = 100 - 25 \\ \: \: \: = 75 \\ mc = \sqrt{75}$

AC=2MC

=2√75

=10√3

=10*1.7

=17 cm

Area of rhombus =1/2(product of its diagonals)

=1/2 * 17*10

=85 cm^2

area of shaded region =314 - 85

= 229 cm^2

I hope it will help you.