Question

A 3cm x 10cm rectangle sits inside a circle with a radius of 12cm. What is the area of the shaded region?

Answer 1

Find the area of the rectangle and the area of the circle:

Formula for the area of a rectangle:

A = l x w [A = area l = length w = width]

You know:

l = 10cm

w = 3 cm Substitute/plug this into the equation

A = l x w

A = 10 x 3

A = 30cm²

Formula for the area of a circle:

A = πr² [A = area r = radius]

You know:

r = 12 cm Substitute/plug this into the equation

A = πr²

A = π(12)²

A = 144π

A = 452.39 cm²

To find the area of the shaded region, subtract the area of the circle (shaded region) by the area of the rectangle (unshaded region)

452.39cm² - 30cm² = 422.39cm²

Answer 2

Area of the shaded region=
`422.16\,cm^2`

Explanation:

Area of the shaded region is :

Area of the circle - Area of the rectangle inside it

Area of the rectangle=
`Length* Width`

`Length=10\,cm\\Width=3\,cm`

Area is:

`10* 3\\\\=30\,cm^2`

Area of the circle=
`\pi * r^2`

`r=12\,cm`

As ,

`\pi =(22)/(7) =3.14`

Area of the Circle =
`3.14*(12* 12)`

`=3.14* 144\\\\=452.16\,cm^2`

Area of the shaded region is:

`=452.16-30\\\\=422.16\,cm^2`