Question

Solve it quickly........​

Answer 1

$\textbf{Answer is in Attachment !}$

Answer 2

Question:

In the figure, arc SBT is one quarter of a circle with centre R and radius 6. If the length plus width of the rectangle ABCR is 8 then the perimeter of the shaded region is

(A) 8 + 3π

(B) 10 + 3π

(C) 14 + 3π

(D) 1 + 6π

(E) 12 + 6π

Solution:

Radius (r) = 6

SR = AC = RT = 6

AR = RC = 8

_____________ [ GIVEN ]

• We have to find the value of the shaded region.

______________________________

Now..

arc SBT = 2πr/4

=> 2π(6)/4

=> 3π

_____________________________

Area of the shaded region = side (SA + AC + CT) + arc SBT

We can write SA = (SR - AR) and CT = (RT - RC)

=> (SR - AR) + AC + (RT - RC) + arc SBT

=> SR - AR + AC + RT - RC + arc SBT

=> SR - (AR + RC) + AC + RT + arc SBT

Put the known values above

=> 6 - (8) + 6 + 6 + 3π

=> - 2 + 12 + 3π

=> 10 + 3π

_____________________________

Option (B) 10 + 3π

_________ [ ANSWER ]

______________________________