How to find the area of a hexagon

Help Questions

SSAT Upper Level Quantitative › How to find the area of a hexagon

Questions 1 - 10

1

Find the area of a regular hexagon that has side lengths of .

$54\sqrt3$

$36\sqrt3$

$48\sqrt3$

Explanation

Use the following formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}\times \text{side}^2$ .

Now, substitute in the length of the side into this equation.

$\text{Area}=\frac{3\sqrt3}{2}\times6^2$

$\text{Area}=\frac{3\sqrt3}{2}\times 36$

$\text{Area}=\frac{108\sqrt3}{2}=54\sqrt3$

2

Find the area of a regular hexagon that has a side length of .

$96\sqrt3$

$48\sqrt3$

$192\sqrt3$

Explanation

Use the following formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}\times \text{side}^2$ .

Now, substitute in the length of the side into this equation.

$\text{Area}=\frac{3\sqrt3}{2}\times 8^2$

$\text{Area}=\frac{3\sqrt3}{2}\times 64$

$\text{Area}=\frac{192\sqrt3}{2}=96\sqrt3$

3

Find the area of a regular hexagon that has a side length of .

$216\sqrt3$

$432\sqrt3$

$108\sqrt3$

Explanation

Use the following formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}\times \text{side}^2$ .

Now, substitute in the length of the side into this equation.

$\text{Area}=\frac{3\sqrt3}{2}\times 12^2$

$\text{Area}=\frac{3\sqrt3}{2}\times 144$

$\text{Area}=\frac{432\sqrt3}{2}=216\sqrt3$

4

Find the area of a regular hexagon that has side lengths of .

$\frac{147}{2}\sqrt3$

$147\sqrt3$

$49\sqrt3$

Explanation

Use the following formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}\times \text{side}^2$ .

Now, substitute in the length of the side into this equation.

$\text{Area}=\frac{3\sqrt3}{2}\times 7^2$

$\text{Area}=\frac{3\sqrt3}{2}\times 49$

$\text{Area}=\frac{147}{2}\sqrt3$

5

Find the area of a regular hexagon with side lengths .

$600\sqrt3$

$1200\sqrt3$

$200\sqrt3$

$450\sqrt3$

Explanation

Use the following formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}\times \text{side}^2$ .

Now, substitute in the length of the side into this equation.

$\text{Area}=\frac{3\sqrt3}{2}\times 20^2$

$\text{Area}=\frac{3\sqrt3}{2}\times 400$

$\text{Area}=\frac{1200\sqrt3}{2}=600\sqrt3$

6

Find the area of a regular hexagon that has side lengths of .

$\frac{3x^2}{2}\sqrt3$

$x^2\sqrt3$

$3x^2\sqrt3$

$\frac{x^2}{2}\sqrt3$

Explanation

Use the following formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}\times \text{side}^2$ .

Now, substitute in the length of the side into this equation.

$\text{Area}=\frac{3\sqrt3}{2}\times x^2$

$\text{Area}=\frac{3x^2}{2}\sqrt3$

7

Find the area of a regular hexagon with side lengths of .

$6t^2\sqrt3$

$12t^2\sqrt3$

$8t^2\sqrt3$

$15t^2\sqrt3$

Explanation

Use the following formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}\times \text{side}^2$ .

Now, substitute in the length of the side into this equation.

$\text{Area}=\frac{3\sqrt3}{2}\times (2t)^2$

$\text{Area}=\frac{3\sqrt3}{2}\times 4t^2$

$\text{Area}=\frac{12t^2\sqrt3}{2}=6t^2\sqrt3$

8

Find the area of a regular hexagon with side lengths of .

$\frac{27m^2}{2}\sqrt3$

$\frac{27m^2}{2}\sqrt2$

$27m^2\sqrt3$

$9m^2\sqrt3$

Explanation

Use the following formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}\times \text{side}^2$ .

Now, substitute in the length of the side into this equation.

$\text{Area}=\frac{3\sqrt3}{2}\times (3m)^2$

$\text{Area}=\frac{3\sqrt3}{2}\times 9m^2$

$\text{Area}=\frac{27m^2}{2}\sqrt3$

9

Find the area of a regular hexagon with side lengths of $\frac{1}{2}$ .

$\frac{3\sqrt3}{8}$

$\frac{\sqrt3}{4}$

$\frac{3\sqrt3}{4}$

$\frac{3\sqrt3}{2}$

Explanation

Use the following formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}\times \text{side}^2$ .

Now, substitute in the length of the side into this equation.

$\text{Area}=\frac{3\sqrt3}{2}\times \left(\frac{1}{2}\right)^2$

$\text{Area}=\frac{3\sqrt3}{2}\times \frac{1}{4}$

$\text{Area}=\frac{3\sqrt3}{8}$

10

Find the area of a regular hexagon with side lengths of .

$96n^2\sqrt3$

$192n^2\sqrt3$

$96n\sqrt3$

$288n^2\sqrt3$

Explanation

Use the following formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}\times \text{side}^2$ .

Now, substitute in the length of the side into this equation.

$\text{Area}=\frac{3\sqrt3}{2}\times (8n)^2$

$\text{Area}=\frac{3\sqrt3}{2}\times 64n^2$

$\text{Area}=\frac{192n^2\sqrt3}{2}=96n^2\sqrt3$

Page 1 of 2

Return to subject