Question

A circle is drawn within a square as shown.

Answer 1

As it is shown in the figure, the length of the square's side  s  is also the length of the circle's diameter  d:

s = d = 28 in.


•  Computing the area of the square:

A₁ = s²

A₁ = 28²

A₁ = 28 × 28

A₁ = 784 in²          ✔


•  Computing the area of the circle:

A₂ = π × r²

A₂ = π × (d/2)²

A₂ = π × (28/2)²

A₂ = π × 14²

A₂ ≈ 3.14 × 14 × 14

A₂ ≈ 615.44 in²          ✔

—————

•  The area of the shaded portion is equal to the difference between the area of the square and the area of circle:

A = A₁ – A₂

A ≈ 784 – 615.44

A ≈ 168.56 in²    <———   this is the answer (1st option).


I hope this helps. =)