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SSAT Upper Level Math : Area of Polygons

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Example Questions

Example Question #1 : How To Find The Area Of A Hexagon

Find the area of a regular hexagon that has side lengths of $\displaystyle 6$.

Possible Answers:

$48\sqrt3$ $\displaystyle 48\sqrt3$

$36\sqrt3$ $\displaystyle 36\sqrt3$

$54\sqrt3$ $\displaystyle 54\sqrt3$

$\displaystyle 36$

Correct answer:

$54\sqrt3$ $\displaystyle 54\sqrt3$

Explanation:

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

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

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

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

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

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

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Example Question #2 : How To Find The Area Of A Hexagon

Find the area of a regular hexagon that has a side length of $\displaystyle 8$.

Possible Answers:

$96\sqrt3$ $\displaystyle 96\sqrt3$

192 $\displaystyle 192$

$192\sqrt3$ $\displaystyle 192\sqrt3$

$48\sqrt3$ $\displaystyle 48\sqrt3$

Correct answer:

$96\sqrt3$ $\displaystyle 96\sqrt3$

Explanation:

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

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

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

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

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

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

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Example Question #3 : How To Find The Area Of A Hexagon

Find the area of a regular hexagon that has a side length of $\displaystyle 12$.

Possible Answers:

432 $\displaystyle 432$

$432\sqrt3$ $\displaystyle 432\sqrt3$

$216\sqrt3$ $\displaystyle 216\sqrt3$

$108\sqrt3$ $\displaystyle 108\sqrt3$

Correct answer:

$216\sqrt3$ $\displaystyle 216\sqrt3$

Explanation:

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

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

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

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

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

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

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Example Question #4 : How To Find The Area Of A Hexagon

Find the area of a regular hexagon that has side lengths of $\displaystyle 7$.

Possible Answers:

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

$147\sqrt3$ $\displaystyle 147\sqrt3$

$49\sqrt3$ $\displaystyle 49\sqrt3$

147 $\displaystyle 147$

Correct answer:

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

Explanation:

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

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

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

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

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

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

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Example Question #11 : Areas And Perimeters Of Polygons

Find the area of a regular hexagon that has side lengths of $\displaystyle 10$.

Possible Answers:

$150\sqrt3$ $\displaystyle 150\sqrt3$

$300\sqrt3$ $\displaystyle 300\sqrt3$

$50\sqrt3$ $\displaystyle 50\sqrt3$

$250\sqrt3$ $\displaystyle 250\sqrt3$

Correct answer:

$150\sqrt3$ $\displaystyle 150\sqrt3$

Explanation:

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

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

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

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

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

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

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Example Question #12 : Areas And Perimeters Of Polygons

Find the area of a regular hexagon with side lengths $\displaystyle 20$.

Possible Answers:

$200\sqrt3$ $\displaystyle 200\sqrt3$

$600\sqrt3$ $\displaystyle 600\sqrt3$

$450\sqrt3$ $\displaystyle 450\sqrt3$

$1200\sqrt3$ $\displaystyle 1200\sqrt3$

Correct answer:

$600\sqrt3$ $\displaystyle 600\sqrt3$

Explanation:

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

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

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

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

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

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

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Example Question #13 : Areas And Perimeters Of Polygons

Find the area of a regular hexagon that has side lengths of $\displaystyle x$.

Possible Answers:

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

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

$x^2\sqrt3$ $\displaystyle x^2\sqrt3$

$3x^2\sqrt3$ $\displaystyle 3x^2\sqrt3$

Correct answer:

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

Explanation:

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

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

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

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

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

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Example Question #14 : Areas And Perimeters Of Polygons

Find the area of a regular hexagon with side lengths of $\displaystyle 2t$.

Possible Answers:

$8t^2\sqrt3$ $\displaystyle 8t^2\sqrt3$

$12t^2\sqrt3$ $\displaystyle 12t^2\sqrt3$

$6t^2\sqrt3$ $\displaystyle 6t^2\sqrt3$

$15t^2\sqrt3$ $\displaystyle 15t^2\sqrt3$

Correct answer:

$6t^2\sqrt3$ $\displaystyle 6t^2\sqrt3$

Explanation:

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

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

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

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

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

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

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Example Question #751 : Geometry

Find the area of a regular hexagon with side lengths of $\displaystyle 3m$.

Possible Answers:

$27m^2\sqrt3$ $\displaystyle 27m^2\sqrt3$

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

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

$9m^2\sqrt3$ $\displaystyle 9m^2\sqrt3$

Correct answer:

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

Explanation:

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

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

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

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

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

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

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Example Question #5 : How To Find The Area Of A Hexagon

Find the area of a regular hexagon with side lengths of $\displaystyle 8n$.

Possible Answers:

$96n^2\sqrt3$ $\displaystyle 96n^2\sqrt3$

$96n\sqrt3$ $\displaystyle 96n\sqrt3$

$192n^2\sqrt3$ $\displaystyle 192n^2\sqrt3$

$288n^2\sqrt3$ $\displaystyle 288n^2\sqrt3$

Correct answer:

$96n^2\sqrt3$ $\displaystyle 96n^2\sqrt3$

Explanation:

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

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

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

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

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

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

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SSAT Upper Level Math : Area of Polygons

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : How To Find The Area Of A Hexagon

Example Question #2 : How To Find The Area Of A Hexagon

Example Question #3 : How To Find The Area Of A Hexagon

Example Question #4 : How To Find The Area Of A Hexagon

Example Question #11 : Areas And Perimeters Of Polygons

Example Question #12 : Areas And Perimeters Of Polygons

Example Question #13 : Areas And Perimeters Of Polygons

Example Question #14 : Areas And Perimeters Of Polygons

Example Question #751 : Geometry

Example Question #5 : How To Find The Area Of A Hexagon

All SSAT Upper Level Math Resources

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