Question

In the figure, arc SBT is a quarter of a circle with center R and radius 6. if the length plus width of rectangle ABCR is 8. Find the perimeter of shaded region.​

Answer 1

⍟CORRECT QUESTION⍟ :–

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

ANSWER :–

LET AR = a and RC = b

We know that –

perimeter of quarter circle = ( 2πr ) / 4 = 3π

AND –

AS = 6 - a , CT = 6 - b , AC = RB = 6 ( radius )

➨ perimeter of the shaded region = AS+AC+CT+C(SBT)

➨ Perimeter = ( 6 - a ) + 6 + ( 6 - b ) + 3π

➨ Perimeter = 18 - ( a + b ) + 3π

● length + width = 8 ( given )

➨ Perimeter = 18 - 8 + 3π

➨ Perimeter = 10 + 3π