# Two circles with the same area are inscribed in a rectangle. If the area of the rectangle is 32, what is the area of one of the circles?

Jun 24, 2016

Area = $4 \pi$

#### Explanation:

The two circles have to fit exactly inside the rectangle (inscribed).

The breadth of the rectangle is the same as the diameter of each
circle, while the length is the same as two diameters.
However, as we are asked for area, it makes more sense to use the radii.

$\text{Breadth" = 2r and "length} = 4 r$

Area= $l \times b$
$2 r \times 4 r = 32$

$8 {r}^{2} = 32$
${r}^{2} = 4$
$r = 2$

Area of one circle$= \pi {r}^{2}$
Area = $\pi \times {2}^{2}$

Area =$4 \pi$