Question

The diagram shows a circle inside a rectangle.... ​

Answer 1

let
`x` = height of rectangle

Given:

• height of rectangle = diameter of circle
• length of rectangle = 3 × height of rectangle

Therefore,

• height of rectangle =
  `x`
• diameter of circle =
  `x`
• radius of circle =
  `(1)/(2)x`
• length of rectangle =
  `3x`

Shaded area = area of rectangle - area of circle

Area of rectangle = length × height

=
`3x * x`

=
`3x^2`

Area of circle =
`\pi r^2`

`=\pi \left((1)/(2)x\right)^2`

`=\frac14\pi x^2`

`\implies \textsf{shaded area}=3x^2-\frac14\pi x^2`

If the radius = 2 cm, then the diameter (
`x`) = 4 cm

Substituting
`x = 4` into the equation:

`\implies \textsf{shaded area}=3(4)^2-\frac14\pi (4)^2`

`\implies \textsf{shaded area}=48-4\pi`

`\implies \textsf{shaded area}=4(12-\pi) \textsf{ cm}^2`