Question

in the given figure op=20cm. in sector a, square opqr is inscribed. then the area of the shaded region____

(a) 200(π+2)cm^2
(b) 100(π+2)cm^2
(c) 200(π-2)cm^2
(d) 100(π-2)cm^2

plz answer fast T^T wit explanation. ​

Answer 1

Answer:

c) 200(π-2)cm^2

Step-by-step explanation:

GIVEN,

OP = 20 CM

TO FIND: AREA OF THE SHADED REGION

FIRST, TAKE OUT THE HYPOTENUSE OF THE SQUARE

IN SQUARE OPQR,

USING PYTHAGORAS THEOREM,

OQ^2 = QP^2 + OP^2

(QP=OP=20CM)

=> OQ^2 = √800(SOLVE THE STEP TO GET √800)

=>OQ = 20√2 CM ( HERE, FROM FIGURE, r IS ALSO 20√2 CM)

THEN,

AREA OF SQUARE = (SIDE)^2

=> (20)^2 CM^2 [(OP)^2]

=> 400 CM^2

NOW,

AREA OF SECTOR OBQA = 1/4 πr^2

=>1/4 π (20√2)^2 CM^2

=> 200π CM^2( after solving)

THEREFORE,

AREA OF SHADED REGION = AREA OF SECTOR - AREA OF SQUARE

=> (200π - 400) CM^2

=> 200(π - 2) CM^2. ANS.

HOPE IT HELPS YOU!!!