Question

Solve the given question

Answer 1

Do the flollowing construction:
Join:
OA and OB


Now,
ABCD is a concyclic quadrilateral,
that means,

angle DAB + angle DCB = 180°

80° + angle ACD + angle ACB = 180°

55° + angle ACB = 100°

angle ACB = 100°-55° = 45°.


Now,
you might know from 9th standard that the angle subtended at center from the arc is twice the angle subtended at the circumference.


Now,

angle AOB = 2 (angle ACB) =2(45°) = 90°.


Given Radius = 7cm.


Therefore,
Area if the sector AOPB will be,


$\frac{90}{360} \pi {r}^{2} \\ \\ \frac{1}{4} \times \frac{22}{7} \times 7 \times 7 = \frac{77}{2} = 38.5$
Therefore the required answer here is 38.5 m^2.