How to find the area of a hexagon - SSAT Upper Level Quantitative (Math)

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Question

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

Answer

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.

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

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

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

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Question

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

Answer

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.

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

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

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

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Question

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

Answer

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.

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

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

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

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Question

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

Answer

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.

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

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

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

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Question

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

Answer

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.

$\text{Area}=\frac{3\sqrt3}{2}\times 10^2$

$\text{Area}=\frac{3\sqrt3}{2}\times 100$

$\text{Area}=\frac{300\sqrt3}{2}=150\sqrt3$

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Question

Find the area of a regular hexagon with side lengths .

Answer

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.

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

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

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

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Question

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

Answer

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.

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

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

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Question

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

Answer

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.

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

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

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

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Question

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

Answer

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.

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

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

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

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Question

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

Answer

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.

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

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

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

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Question

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

Answer

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.

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

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

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

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Question

Find the area of a regular hexagon with side lengths .

Answer

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.

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

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

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

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