# Question #a9c2e

May 29, 2017

Yes, there is a way that you could construct a circle that has the exact same area as a triangle or quadrilateral. See explanation. (I used a perfect square for my explanation).

#### Explanation:

Yes, I believe so. the way you could do this is by making the lengths of the sides of the square as so that they derive from $\pi$.

$A = \pi {r}^{2}$

$A = l \times w$

$A = \frac{b h}{2}$

we could make the side lengths of the square $\pi$ units, and the other side the ${\text{radius of the circle}}^{2}$

$A = \pi {r}^{2}$
$A = \pi {4}^{2}$
$= 50.2655$

$A = l \times w$
$A = \pi \times 16$
$= 50.2655$

The same could be done with a Triangle.

$A = \frac{b h}{2}$
$A = \frac{\pi 32}{2}$
$A = \frac{100.531}{2}$