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SSAT Middle Level Math : Geometry

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

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Example Questions

Example Question #1 : How To Find The Perimeter Of A Triangle

A triangle has sides feet, feet, and feet. Calculate its perimeter.

Possible Answers:

$360 \;ft$

$25 \;ft$

$100 \;ft$

$50 \;ft$

$240 \;ft$

Correct answer:

$50 \;ft$

Explanation:

The perimeter of any figure is the sum of the lengths of the sides: $12 + 18 + 20 = 50 \;ft$ .

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Example Question #3 : How To Find Perimeter Of A Triangle

A right triangle with hypotenuse 65 has one leg of length 60. What is its perimeter?

Possible Answers:

325

150

125

300

185

Correct answer:

150

Explanation:

By the Pythagorean Theorem, if and are the legs of a right triangle and is its hypotenuse, then

$a^{2} + b^{2} = c^{2}$ .

Set b = 60, c= 65 and solve for :

$a^{2} + 60^{2} = 65^{2}$

$a^{2} + 3,600 = 4,225$

$a^{2} + 3,600 -3,600 = 4,225 -3,600$

$a^{2} = 625$

$\sqrt{a^{2}} =\sqrt{ 625}$

a = 25

The perimeter of the triangle - the sum of the sidelengths - is

P = 25 + 60 + 65 = 150 .

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Example Question #1 : Plane Geometry

What is the perimeter of an equilateral triangle with a side length ?

Possible Answers:

Correct answer:

Explanation:

The perimeter is equal to the sum of the length of the sides. An equilateral triangle has three sides with equal lengths.

P=4+4+4=12

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Example Question #3 : How To Find The Perimeter Of A Triangle

Find the perimeter of a triangle with sides 8cm , 9cm , and 11cm .

Possible Answers:

19cm

28cm

24cm

30cm

16cm

Correct answer:

28cm

Explanation:

Perimeter involves adding up all of the sides of the shapes; in this case, it's a triangle. Perimeter equals 9+8+11 . Therefore, the answer is 28cm .

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Example Question #11 : How To Find Perimeter Of A Triangle

A right triangle has legs feet and feet long. What is its perimeter, in inches?

Possible Answers:

$864 \textrm{ in}$

$252 \textrm{ in}$

$504 \textrm{ in}$

$432 \textrm{ in}$

$216 \textrm{ in}$

Correct answer:

$432 \textrm{ in}$

Explanation:

The length of the hypotenuse of the triangle can be found using the Pythagorean Theorem. Substitute a = 9,b= 12 :

$c = \sqrt{a ^{2} + b^{2} } =\sqrt{9 ^{2} +12^{2} } = \sqrt{81+144} = \sqrt{225} = 15$ feet

Its perimeter is P = 9 + 12 + 15 = 36 feet. Multiply by 12 to get the perimeter in inches:

$36 \times 12 = 432$ inches

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Example Question #2 : How To Find The Perimeter Of A Triangle

An equilateral triangle has perimeter 73.5 centimeters. How long is one side?

Possible Answers:

$24.5 \textrm{ cm}$

$36.75 \textrm{ cm}$

$29.4 \textrm{ cm}$

$18.375 \textrm{ cm}$

$14.7 \textrm{ cm} ^{2}$

Correct answer:

$24.5 \textrm{ cm}$

Explanation:

An equilateral triangle has three sides of equal measure, so divide its perimeter by :

$73.5 \div 3 =24.5 \textrm{ cm}$

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Example Question #13 : How To Find Perimeter Of A Triangle

Find the perimeter of an equilateral triangle with a base of 11in.

Possible Answers:

$33\text{in}$

$22\text{in}$

$121\text{in}$

$\text{There is not enough information to solve the problem.}$

$31\text{in}$

Correct answer:

$33\text{in}$

Explanation:

To find the perimeter of a triangle, we will use the following formula:

P = a+b+c

where a, b, and c are the lengths of the sides of the triangle.

Now, we know the base of the equilateral triangle is 11in. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 11in.

So, we can substitute. We get

$P = 11\text{in} + 11\text{in} + 11\text{in}$

$P = 33\text{in}$

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Example Question #11 : How To Find Perimeter Of A Triangle

Which of these choices can the perimeter of an isosceles triangle possibly be if you know that two sides have lengths 12 and 13?

Possible Answers:

Correct answer:

Explanation:

An isosceles triangle has two sides of equal length. If two sides of an isoscelese triangle are of length 12 and 13, then the third must be of length 12 or 13.

This makes the perimeter either

12+12+13=37

12+13+13=38

Of our choices, we choose 38.

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Example Question #1 : How To Find The Perimeter Of A Square

Florence wants to build a fence to surround her square garden. The garden has an area of 16 square yards. How much fencing will she need?

Possible Answers:

Correct answer:

Explanation:

So this question requires you to know the formula for area for a square which is side squared.

Thus, $16 = s^{2}$ , so one side is the square root of 16, or 4.

To figure out the perimeter, add up all of the sides of the square which are all the same (4).

4 + 4 + 4 + 4 = 16

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Example Question #2 : How To Find The Perimeter Of A Square

A square has perimeter 89.4 centimeters. What is the length of one side?

Possible Answers:

$32.8 \textrm{ cm}$

$29.8 \textrm{ cm}$

$22.35 \textrm{ cm}$

$24.25 \textrm{ cm}$

$44.7 \textrm{ cm}$

Correct answer:

$22.35 \textrm{ cm}$

Explanation:

A square has four sides of equal measure, so divide its perimeter by 4:

$89.4 \div 4 = 22.35 \textrm{ cm}$

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SSAT Middle Level Math : Geometry

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #1 : How To Find The Perimeter Of A Triangle

Example Question #3 : How To Find Perimeter Of A Triangle

Example Question #1 : Plane Geometry

Example Question #3 : How To Find The Perimeter Of A Triangle

Example Question #11 : How To Find Perimeter Of A Triangle

Example Question #2 : How To Find The Perimeter Of A Triangle

Example Question #13 : How To Find Perimeter Of A Triangle

Example Question #11 : How To Find Perimeter Of A Triangle

Example Question #1 : How To Find The Perimeter Of A Square

Example Question #2 : How To Find The Perimeter Of A Square

All SSAT Middle Level Math Resources

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