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SSAT Upper Level Math : Geometry

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 #3 : Perimeter Of Polygons

A hexagon with perimeter of 48 has three congruent sides of 2t+3 . Its other three sides are congruent to each other with the length of 2t-7 . Find .

Possible Answers:

Correct answer:

Explanation:

The perimeter of a polygon is the sum of the lengths of its sides. Since three sides are congruent with the length of 2t+3 and the rest of the sides have the length of 2t-7 we can write:

Perimeter=3(2t+3)+3(2t-7)=48

Now we should solve the equation for :

$6t+9+6t-21=48\Rightarrow 12t-12=48\Rightarrow 12t=60\Rightarrow t=5$

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Example Question #741 : Geometry

A regular pentagon has sidelength one foot; a regular hexagon has sidelength ten inches. The perimeter of a regular octagon is the sum of the perimeters of the pentagon and the hexagon. What is the measure of one side of the octagon?

Possible Answers:

$18 \textrm{ in }$

$15 \textrm{ in }$

$12 \textrm{ in }$

$16 \textrm{ in }$

$10 \textrm{ in }$

Correct answer:

$15 \textrm{ in }$

Explanation:

A regular polygon has all of its sides the same length. The pentagon has perimeter $5 \times 12 \textrm{ in } = 60 \textrm{ in }$ ; the hexagon has perimeter $6 \times 10 \textrm{ in } = 60 \textrm{ in }$ . The sum of the perimeters is $60 \textrm{ in } + 60 \textrm{ in }= 120 \textrm{ in }$ , which is the perimeter of the octagon; each side of the octagon has length $120 \textrm{ in } \div 8 = 15 \textrm{ in }$ .

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Example Question #6 : How To Find The Perimeter Of A Hexagon

Find the perimeter of a hexagon with a side length of 6a+b .

Possible Answers:

36a+b

12a+6b

6a+6b

36a+6b

36a+36b

Correct answer:

36a+6b

Explanation:

A hexagon has six sides. The perimeter of a hexagon is:

P=6s

Substitute the side length.

P=6s=6(6a+b)=36a+6b

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Example Question #6 : Areas And Perimeters Of Polygons

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

Possible Answers:

$36\sqrt3$

$54\sqrt3$

$48\sqrt3$

Correct answer:

$54\sqrt3$

Explanation:

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

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

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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Example Question #7 : Areas And Perimeters Of Polygons

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

Possible Answers:

$96\sqrt3$

$48\sqrt3$

192

$192\sqrt3$

Correct answer:

$96\sqrt3$

Explanation:

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

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

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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Example Question #741 : Geometry

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

Possible Answers:

$216\sqrt3$

$432\sqrt3$

$108\sqrt3$

432

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 #1 : How To Find The Area Of A Hexagon

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

Possible Answers:

$49\sqrt3$

147

$147\sqrt3$

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

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 #743 : Geometry

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

Possible Answers:

$250\sqrt3$

$150\sqrt3$

$300\sqrt3$

$50\sqrt3$

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 #744 : Geometry

Find the area of a regular hexagon with side lengths .

Possible Answers:

$450\sqrt3$

$600\sqrt3$

$1200\sqrt3$

$200\sqrt3$

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 #1 : How To Find The Area Of A Hexagon

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

Possible Answers:

$3x^2\sqrt3$

$x^2\sqrt3$

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

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

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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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Geometry

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #3 : Perimeter Of Polygons

Example Question #741 : Geometry

Example Question #6 : How To Find The Perimeter Of A Hexagon

Example Question #6 : Areas And Perimeters Of Polygons

Example Question #7 : Areas And Perimeters Of Polygons

Example Question #741 : Geometry

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

Example Question #743 : Geometry

Example Question #744 : Geometry

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

All SSAT Upper Level Math Resources

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