SSAT Elementary Level Math : Plane Geometry

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

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Example Questions

Example Question #631 : Plane Geometry

An equilateral triangle is a type of triangle that has sides that are each of the same length. If one of the sides of an equilateral triangle is \displaystyle 3 units long, what is the perimeter of the triangle?

Possible Answers:

\displaystyle 9 units

\displaystyle 12 units

\displaystyle 3 units

\displaystyle 15 units

\displaystyle 6 units

Correct answer:

\displaystyle 9 units

Explanation:

Since an equilateral triangle has three equal sides, the total perimeter of the triangle is \displaystyle 9 units, since each side is \displaystyle 3 units long and \displaystyle 3+3+3=9.

Example Question #5787 : Ssat Elementary Level Quantitative (Math)

A triangle has sides of three different lengths. One of its sides is \displaystyle 5 units long. Another of its sides is \displaystyle 3 units long. The third side is of a length that is the average of its other two sides. What is the perimeter of this triangle?

Possible Answers:

\displaystyle 8

\displaystyle 7

\displaystyle 12

\displaystyle 9

\displaystyle 17

Correct answer:

\displaystyle 12

Explanation:

We know two of the lengths of the triangle's sides: \displaystyle 5 and \displaystyle 3. We are also told that its third side's length is an average of its other two sides. We can find the average of \displaystyle 5 and \displaystyle 3 by adding them together and dividing by two: \displaystyle 5+3=8 and \displaystyle 8\div2=4, so the triangle's third side has a length of \displaystyle 4. We can now find the perimeter of the triangle by adding up the lengths of its sides: \displaystyle 3+4+5=12, so the perimeter of the triangle is \displaystyle 12.

Example Question #632 : Plane Geometry

What is the perimeter of a triangle with a side length of \displaystyle 4?

Possible Answers:

\displaystyle 18

\displaystyle 16

\displaystyle 8+4\sqrt2

\displaystyle 12

Correct answer:

Explanation:

There is no certainty of the type of triangle described in this situation.  This can be an equilateral triangle, isosceles triangle, scalene triangle, or a right triangle.

There is not enough information to determine the perimeter since we only have the dimension of one side.

Example Question #5792 : Ssat Elementary Level Quantitative (Math)

Find the perimeter of a right isosceles triangle with a hypotenuse of \displaystyle 2.

Possible Answers:

\displaystyle 4

\displaystyle \sqrt2+4

\displaystyle 2\sqrt2 + 2

\displaystyle 2\sqrt2

\displaystyle \sqrt2 + 2

Correct answer:

\displaystyle 2\sqrt2 + 2

Explanation:

Write the Pythagorean Theorem.

\displaystyle a^2+b^2 =c^2

In an isosceles triangle, the legs are equal:  \displaystyle a=b

\displaystyle a^2+a^2 = 2^2

Solve for the leg.

\displaystyle 2a^2 = 4

\displaystyle a^2 =2

\displaystyle a=\sqrt{2}=b

The perimeter is the sum of the legs and the hypotenuse.

\displaystyle a+b+h= \sqrt2+\sqrt2+2=2\sqrt2 + 2

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

A triangle has the side lengths \displaystyle 8, \displaystyle 7, and \displaystyle 13.  What is the perimeter of the triangle?

Possible Answers:

\displaystyle \frac{28}{13}

\displaystyle \frac{25}{13}

\displaystyle 14

\displaystyle 28

\displaystyle 12

Correct answer:

\displaystyle 28

Explanation:

The perimeter of a triangle is the sum of the three sides.

Add the lengths together to find the perimeter.

\displaystyle P=8+7+13 = 15+13 = 28

Example Question #633 : Plane Geometry

What is the PERIMETER of the triangle in the figure?

 Screen_shot_2014-01-31_at_4.18.55_pm

Possible Answers:

\displaystyle 12 cm

\displaystyle 34 cm

\displaystyle 10 cm

\displaystyle 7 cm

\displaystyle 12 cm

Correct answer:

\displaystyle 10 cm

Explanation:

Because the question asks you to find the PERIMETER of the triangle, you are looking to figure out the distance around the outside of the triangle. You find the perimeter of triangles simply by adding the length of the three sides together. So the correct answer here is \displaystyle 3 \: cm + 3 \: cm + 4 \: cm, or \displaystyle 10 cm.

Example Question #634 : Plane Geometry

What is the PERIMETER of the triangle in the figure?

Screen_shot_2014-01-31_at_4.17.07_pm

Possible Answers:

\displaystyle 160 cm

\displaystyle 150 cm

\displaystyle 200 cm

\displaystyle 240 cm

\displaystyle 170 cm

Correct answer:

\displaystyle 170 cm

Explanation:

Because the question asks you to find the PERIMETER of the triangle, you are looking to figure out the distance around the outside of the triangle. You find the perimeter of triangles simply by adding the length of the three sides together. So the correct answer here is \displaystyle 50\: cm + 50\: cm + 70\: cm, or \displaystyle 170 cm.

Example Question #633 : Plane Geometry

What is the PERIMETER of the triangle in the figure? 

Screen_shot_2014-01-31_at_4.10.07_pm

Possible Answers:

\displaystyle 25 cm

\displaystyle 150 cm

\displaystyle 100 cm

\displaystyle 80 cm

\displaystyle 50 cm

Correct answer:

\displaystyle 80 cm

Explanation:

Because the question asks you to find the PERIMETER of the triangle, you are looking to figure out the distance around the outside of the triangle. You find the perimeter of triangles simply by adding the length of the three sides together. Then the correct answer here is \displaystyle 25 \: cm + 25 \: cm + 30\: cm, or 80 cm.

Example Question #43 : Triangles

The perimeter of an equilateral triangle is \displaystyle 24 mm.  Which choice shows the correct side lengths?

Possible Answers:

\displaystyle 6 \: mm\ast 10\: mm\ast 8\: mm

\displaystyle 8 \: mm\ast 8\: mm\ast 8\: mm

\displaystyle 9 \: mm+8\: mm+7\: mm

\displaystyle 6 \: mm+10\: mm+8\: mm

\displaystyle 8 \: mm+8\: mm+8\: mm

Correct answer:

\displaystyle 8 \: mm+8\: mm+8\: mm

Explanation:

When finding the perimeter of any triangle, you will need to add all three sides. In this case, it is important to note that this is the perimeter of an equilateral triangle. An equilateral triangle has \displaystyle 3 congruent/equal sides. All the choices add up to \displaystyle 24 mm (except the choice that shows multiplication instead of addition), but only one choice shows \displaystyle 3 equal sides that add up to      \displaystyle 24mm:

\displaystyle 8 \: mm+8\: mm+8\: mm

Example Question #21 : How To Find The Perimeter Of A Triangle

What is the PERIMETER of the triangle in the figure? Screen_shot_2014-01-31_at_4.13.52_pm

Possible Answers:

\displaystyle 90 cm

\displaystyle 15 cm

\displaystyle 45 cm

\displaystyle 25 cm

30 cm

Correct answer:

\displaystyle 45 cm

Explanation:

Because the question asks you to find the PERIMETER of the triangle, you are looking to figure out the distance around the outside of the triangle. You find the perimeter of triangles simply by adding the length of the three sides together. So the correct answer here is \displaystyle 15\: cm + 15 \: cm + 15 \: cm, or \displaystyle 45 cm.

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