Question

In the figure below, O is the centre of the circle
and OABC is a square. P and Q are the midpoints
of OC and OA, respectively. The area of the square
(in cm), if the area of the shaded part is 38,5 cm?,
(a) 49
(c) 144
(b) 81
(d) 196​

Answer 1

the area of shades part is 49

Answer 2

Answer:

Area of the square = 196 cm²

Step-by-step explanation:

Given data

In given figure O is the center of the circle and OABC is a square

P and Q are the mid points of OC and OA respectively

and are of the shaded part is 38.5 cm²  

here we need to find area of the square  

from the figure we can conclude that QOP is a sector and ∠POQ = 90°  and OP is the radius let r be the radius  

area of the sector = area of the shaded part

       ⇒     $\frac{90}{360} (\pi r^{2}) =$ 38.5 cm  

       ⇒     $\frac{1}{4} (\frac{22}{7} ) r^{2} = 38.5$  

       ⇒     r² = $\frac{38.5 (7)(4)}{22}$  

       ⇒     r² = $\frac{1078}{22}$ = 49

       ⇒     r  =  7 cm  

from given data P is mid point of the OC then OP will be equals to PC,

⇒  PC = 7 cm

⇒  OC  = OP + PC = 7 + 7 = 14 cm

⇒ side of the square OC = 14 cm

⇒ Area of the square = a²        [ where a is side of the square]  

                                  = 14 × 14 =  196 cm²