Question

The diagram shows a square of side length 10 cm. A quarter circle, of radius 10 cm is drawn from each vertex of a square. find the exact area of the shaded region.


This is from As level Book by Sue Pemberton. page 110 Q12

Answer 1

Answer:

this is your answer..

Hope it helps you..

Answer 2

Answer:

100 ( π/3  + 1 - √3) cm²

31.5 cm²

Step-by-step explanation:

we need to find Area of A

As this is a square and radius are all equal

Hence region mentioned have equal areas

B = C = D = E

F = G = H = I

Point F if joined  with both bottom vertex of square  then its = 10

as its on arc of radius = 10

and hence form an equilateral triangle

so Area of A + D + E + H =  (60/360) π 10² + (60/360) π 10²  - (√3 / 4)10²

= 100 ( π/3 - √3 / 4)

Area of A + D + E + H  + C + G  =  (90/360) π 10² = 100 π/4

Area of C + G = 100 π/4 - 100 ( π/3 - √3 / 4)

= 100 ( √3 / 4  - π/12)

C+ G = D+H = E + I = B + F

=> B + C + D + E + F + G + H = 4 * 100 ( √3 / 4  - π/12) =  100 (√3  - π/3)

Area of A  =  Area of Square - Area of ( B + C + D + E + F + G + H)

= 10² - 100 (√3  - π/3)

= 100 ( π/3  + 1 - √3)

= 31.5 cm²