SSAT Middle Level Math : Geometry

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

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Example Questions

Example Question #201 : Geometry

Measured in units, the bases of a trapezoid are  and , the lengths are , and the height is unknown.  What is the perimeter of the trapezoid in units?

Possible Answers:

Impossible to calculate.

Correct answer:

Explanation:

The perimeter is solved by adding the two bases together,  and , along with both the lengths, .

Therefore the equation becomes,

Example Question #11 : How To Find The Perimeter Of A Trapezoid

Measured in units, the bases of a trapezoid are  and , the lengths are , and the height is unknown.  What is the perimeter of the trapezoid in units?

Possible Answers:

Impossible to calculate

Correct answer:

Explanation:

The perimeter is solved by adding the two bases together,  and , along with both the lengths, .

Therefore the equation becomes,

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

Find the perimeter of the trapezoid:
Question_12

Possible Answers:

Correct answer:

Explanation:

The perimeter of any shape is equal to the sum of the lengths of its sides:

Example Question #11 : How To Find The Perimeter Of A Trapezoid

Trapezoid

Find the perimeter of the given trapezoid if 

Possible Answers:

Correct answer:

Explanation:

In order to find the perimeter, we must find the sum of the outer edges: 

Trapezoid_labeled

Notice that we didn't use height in our calculation. 

Example Question #19 : How To Find The Perimeter Of A Trapezoid

Trapezoid

Find the perimeter of the given trapezoid if 

Possible Answers:

Correct answer:

Explanation:

In order to find the perimeter, find the sum of the outer edges:

Trapezoid_labeled

Notice that we didn't use height in our calculation. 

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

Trapezoid

The above diagram depicts a rectangle  with isosceles triangle .  is the midpoint of . What is the ratio of the area of the orange trapezoid to that of the white triangle?

Possible Answers:

More information is needed to answer this question.

Correct answer:

Explanation:

We can simplify this problem by supposing that the length of one leg of a triangle is 2. Then the other leg is 2, and the area of the triangle is 

Since  is the midpoint of  , . Also, since opposite sides of a rectangle are congruent,

.

This makes the trapezoid one with height 2 and bases 2 and 4, so 

The ratio of the area of the trapezoid to that of the triangle is 6 to 2, which simplifies to 3 to 1.

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

Q_10

Find the area of the trapezoid above.

Note: Image not drawn to scale.

Possible Answers:

Correct answer:

Explanation:

The area of a trapezoid is equal to the average of the length of the two bases multiplied by the height.

The formula to find the area of a trapezoid is:  

In this problem, the lengths of the bases are  and  Their average is . The height of the trapezoid is 

Remember: the answer to the problem should have units in cm2 .

Example Question #201 : Geometry

Find the area of a trapezoid with a height of  and base lengths of  and , respectively.

Possible Answers:

Correct answer:

Explanation:

The area  of a trapezoid is equal to the average of its two bases ( and ) multiplied by its height . Therefore:

Example Question #201 : Geometry

Find the area of a trapezoid with a height of  and base lengths of  and , respectively.

Possible Answers:

Correct answer:

Explanation:

The area  of a trapezoid is equal to the average of its two bases ( and ) multiplied by its height . Therefore:

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

Trapezoid

 

What is the area of the above trapezoid?

Possible Answers:

Correct answer:

Explanation:

To find the area of a trapezoid, multiply one half (or 0.5, since we are working with decimals) by the sum of the lengths of its bases (the parallel sides) by its height (the perpendicular distance between the bases). This quantity is

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