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SSAT Middle Level Math : Quadrilaterals

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

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Example Question #153 : Plane 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,

5+2+20+20=47

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Example Question #154 : Plane 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,

5+2+10+10=27

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Example Question #155 : Plane 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,

5+10+10+10=35

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Example Question #156 : Plane 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,

10+15+10+10=45

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

Find the perimeter of the trapezoid:
Question_12

Possible Answers:

$\small 21$

$\small 40$

$\small 23.5$

$\small 26$

Correct answer:

$\small 21$

Explanation:

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

$\small P=4+6+3+8=21$

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Example Question #161 : Plane Geometry

Trapezoid

Find the perimeter of the given trapezoid if $l=9, h=7, b_{1}=8, b_{2}=10$

Possible Answers:

Correct answer:

Explanation:

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

Trapezoid_labeled

9+8+ 9+10=36

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

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

Trapezoid

Find the perimeter of the given trapezoid if $l=6, h=4, b_{1}=2, b_{2}=5$

Possible Answers:

Correct answer:

Explanation:

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

Trapezoid_labeled

6+2+6+5=19

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

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

Trapezoid

The above diagram depicts a rectangle RECT with isosceles triangle $\Delta ECM$ . is the midpoint of $\overline{CT}$ . What is the ratio of the area of the orange trapezoid to that of the white triangle?

Possible Answers:

9:2

3:1

7:2

4:1

More information is needed to answer this question.

Correct answer:

3:1

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

$A = \frac {1}{2} \cdot 2 \cdot 2 = 2$

Since is the midpoint of $\overline{CT}$ , MT = 2 . Also, since opposite sides of a rectangle are congruent,

RE = CT = CM + MT = 2 + 2 = 4 .

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

$A = \frac {1}{2} \cdot (2 + 4) \cdot 2 = 6$

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

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

Find the area of the trapezoid above.

Note: Image not drawn to scale.

Possible Answers:

$120\: cm^{2}$

$120\: cm$

$80\: cm$

$200\: cm^{2}$

$160\: cm$

Correct answer:

$120\: cm^{2}$

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: $\left (\frac{base_{1} + base_{2}}{2}\right )* height$

In this problem, the lengths of the bases are $10\: cm$ and $20\: cm.$ Their average is $15\: cm$ . The height of the trapezoid is $8\: cm.$

$15\: cm\ast 8\: cm=120\: cm$

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

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

Find the area of a trapezoid with a height of $5\:cm$ and base lengths of $4\:cm$ and $8\:cm$ , respectively.

Possible Answers:

$15\:cm^{2}$

$10\:cm^{2}$

$22\:cm^{2}$

$30\:cm^{2}$

$17\:cm$

Correct answer:

$30\:cm^{2}$

Explanation:

The area of a trapezoid is equal to the average of its two bases ( $b_{1}$ and $b_{2}$ ) multiplied by its height . Therefore:

$A=\frac{1}{2}(b_{1}+b_{2})h$

$A=\frac{1}{2}(4\:cm+8\:cm)5\:cm$

$A=\(6\:cm)5\:cm$

$A=30\:cm^{2}$

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SSAT Middle Level Math : Quadrilaterals

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #153 : Plane Geometry

Example Question #154 : Plane Geometry

Example Question #155 : Plane Geometry

Example Question #156 : Plane Geometry

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

Example Question #161 : Plane Geometry

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

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

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

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

All SSAT Middle Level Math Resources

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