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SSAT Upper Level Math : Areas and Perimeters of Polygons

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

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Area Of Polygons

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

Possible Answers:

432

$216\sqrt3$

$432\sqrt3$

$108\sqrt3$

Correct answer:

$216\sqrt3$

Explanation:

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

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

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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Example Question #2 : Area Of Polygons

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

Possible Answers:

$147\sqrt3$

147

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

$49\sqrt3$

Correct answer:

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

Explanation:

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

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

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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Example Question #1 : Area Of Polygons

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

Possible Answers:

$50\sqrt3$

$150\sqrt3$

$250\sqrt3$

$300\sqrt3$

Correct answer:

$150\sqrt3$

Explanation:

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

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

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

Find the area of a regular hexagon with side lengths .

Possible Answers:

$600\sqrt3$

$200\sqrt3$

$1200\sqrt3$

$450\sqrt3$

Correct answer:

$600\sqrt3$

Explanation:

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

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

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

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

Possible Answers:

$3x^2\sqrt3$

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

$x^2\sqrt3$

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

Correct answer:

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

Explanation:

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

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

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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Example Question #3 : Area Of Polygons

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

Possible Answers:

$15t^2\sqrt3$

$6t^2\sqrt3$

$12t^2\sqrt3$

$8t^2\sqrt3$

Correct answer:

$6t^2\sqrt3$

Explanation:

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

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

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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Example Question #4 : Area Of Polygons

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

Possible Answers:

$9m^2\sqrt3$

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

$27m^2\sqrt3$

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

Correct answer:

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

Explanation:

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

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

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

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

Possible Answers:

$192n^2\sqrt3$

$96n\sqrt3$

$288n^2\sqrt3$

$96n^2\sqrt3$

Correct answer:

$96n^2\sqrt3$

Explanation:

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

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

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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Example Question #751 : Geometry

Find the area of a regular hexagon with side lengths 12c .

Possible Answers:

$216c^2\sqrt3$

$108c^2\sqrt3$

$432c^2\sqrt3$

$216\sqrt3$

Correct answer:

$216c^2\sqrt3$

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.

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

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

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

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Example Question #12 : How To Find The Area Of A Hexagon

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

Possible Answers:

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

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

$\frac{\sqrt3}{4}$

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

Correct answer:

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

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.

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

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

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

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SSAT Upper Level Math : Areas and Perimeters of Polygons

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : Area Of Polygons

Example Question #2 : Area Of Polygons

Example Question #1 : Area Of Polygons

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 : Area Of Polygons

Example Question #4 : Area Of Polygons

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

Example Question #751 : Geometry

Example Question #12 : How To Find The Area Of A Hexagon

All SSAT Upper Level Math Resources

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