Question

calculate the area of shaded region if in given figure where ABCD is a square of side 16 centimetre

Answer 1

Refer the attachment for figure.


Join BD

Now, Consider the quadrant ADB and ∆ADB


area of quadrant ADB - area of triangle ADB = area of half white portion.

Area of quadrant ADB = πr²/4

r = 16 cm

=> Area of quadrant ADB = π16²/4

=> area of quadrant ADB = 256π/4

=> area of quadrant ADB = 64π cm²

area of ∆ADB = 1/2 × 16 × 16 = 8 × 16 = 128 cm²

So, area of half white portion = 64π - 128

=> area of half white portion = 64(π - 2)

So, area of full white portion = 2 × 64(π - 2)

=> area of full white portion = 128(π - 2)


Now, area of shaded = area of square - area of white

area of square = 16² = 256 cm²

Hence, area of shaded = 256 - 128(π - 2)

=> area of shaded = 256 - 128π + 256

=> area of shaded = 512 - 128π

=> area of shaded = 128(4 - π)


Answer :- 128(4 - π)



You can further elaborate the answer,


512 - 128π

= 512 - 128 × 22/7

= 512 - 402.28 (approx)

= 109.72 cm² (approx)