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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

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

Find the area of the trapezoid:

Question_7

Possible Answers:

Correct answer:

Explanation:

The area of a trapezoid can be determined using the equation $A=\frac{1}{2}(b_1+b_2)h$ .

$A=\frac{1}{2}(6+8)(4)$

$A=\frac{1}{2}(14)(4)$

A=(7)(4)=28

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

Trapezoid

What is the area of the trapezoid?

Possible Answers:

$105\textrm{ m}^{2}$

$63\textrm{ m}^{2}$

$135\textrm{ m}^{2}$

$99\textrm{ m}^{2}$

$198\textrm{ m}^{2}$

Correct answer:

$99\textrm{ m}^{2}$

Explanation:

To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.

$A = \frac{1}{2} \cdot (7 + 15) \cdot 9 = \frac{1}{2} \cdot 22 \cdot 9 = 99 \textrm{ m}^2$

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Example Question #213 : Geometry

Trapezoid

The above diagram depicts a rectangle RECT with isosceles triangle $\Delta ECM$ . If is the midpoint of $\overline{CT}$ , and the area of the orange region is , then what is the length of one leg of $\Delta ECM$ ?

Possible Answers:

$\sqrt {96}$

$\sqrt {48}$

$\sqrt {54}$

$\sqrt {108}$

Correct answer:

$\sqrt {48}$

Explanation:

The length of a leg of $\Delta ECM$ is equal to the height of the orange region, which is a trapezoid. Call this length/height .

Since the triangle is isosceles, then CM = h , and since is the midpoint of $\overline{CT}$ , MT = h . Also, since opposite sides of a rectangle are congruent,

RE = CT = CM + MT = h + h = 2h

Therefore, the orange region is a trapezoid with bases and and height . Its area is 72, so we can set up and solve this equation using the area formula for a trapezoid:

$\frac{1}{2} (B + b)h = 72$

$\frac{1}{2} (2h + h)h = 72$

$\frac{1}{2} (3h )h = 72$

$\frac{3}{2}h^{2} = 72$

$\frac{3}{2}h^{2} \cdot \frac{2}{3} = 72 \cdot \frac{2}{3}$

$h^{2}= 48$

$h = \sqrt {48}$

This is the length of one leg of the triangle.

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Example Question #214 : Geometry

A trapezoid has a height of inches and bases measuring inches and inches. What is its area?

Possible Answers:

$1,500\; \textrm{in}^{2}$

$900\; \textrm{in}^{2}$

$864\; \textrm{in}^{2}$

$600\; \textrm{in}^{2}$

$750\; \textrm{in}^{2}$

Correct answer:

$750\; \textrm{in}^{2}$

Explanation:

Use the following formula, with B = 36,b = 24,h=25 :

$A = \frac{1}{2} (B+b)h = \frac{1}{2} (36+24) \cdot 25 = 750$

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Example Question #2 : How To Find The Area Of A Trapezoid

What is the area of a trapezoid with height 20 inches and bases of length 100 and 200?

Possible Answers:

$3,000\; \textrm{in}^{2}$

$1,000\; \textrm{in}^{2}$

$4,000\; \textrm{in}^{2}$

$6,000\; \textrm{in}^{2}$

$2,000\; \textrm{in}^{2}$

Correct answer:

$3,000\; \textrm{in}^{2}$

Explanation:

Set B=200 , b=100 , h = 20 .

The area of a trapezoid can be found using this formula:

$A = \frac{1}{2} (B+b)h = \frac{1}{2} (200+100) \cdot 20 = 3,000$

The area is 3,000 square inches.

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Example Question #216 : Geometry

Lines

Figure NOT drawn to scale.

AE = 80, AB = x, BC = x + 4, CD = 2x+1, DE = x-6

Evaluate .

Possible Answers:

12.8

17.8

13.8

16.2

15.2

Correct answer:

16.2

Explanation:

By the Segment Addition Postulate,

AB + BC + CD + DE = AE

x + (x+4) + (2x+1) + (x-6) = 80

5x-1= 80

5x-1+1 = 80+1

5x = 81

$5x \div 5 = 81 \div 5$

x = 16.2

AB = x = 16.2

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Example Question #1 : How To Find Length Of A Line

A right triangle has one leg with a length of 6 feet and a hypotenuse of 10 feet. What is the length of the other leg?

Possible Answers:

$8\ \text{ft}$

$6\ \text{ft}$

$4\ \text{ft}$

$5\ \text{ft}$

$10\ \text{ft}$

Correct answer:

$8\ \text{ft}$

Explanation:

In geometry, a right angle triangle can occur with the ratio of 3:4:5 in which 3 and 4 are each leg lengths, and 5 is the hypotenuse.

When you know the length of two sides of a right angle triangle like this, you can calculate the third side using this ratio.

Here, the ratio is:

6:x:10

This is double the 3:4:5 ratio. Therefore, we should multiply 4 by 2 in order to solve for the missing leg, which would be a value of 8 feet.

Another way to solve is to use the Pythagorean Theorem: a^2+b^2=c^2 .

We know that one leg is 6 feet and the hypotenuse is 10 feet.

(6)^2+b^2=(10)^2

36+b^2=100

b^2=64

$b=\sqrt{64}=8$

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Example Question #218 : Geometry

The radius of a circle is 6 inches. What is one-third of the diameter?

Possible Answers:

$2\ \textup{inches}$

$7\ \textup{inches}$

$12\ \textup{inches}$

$4\ \textup{inches}$

$6\ \textup{inches}$

Correct answer:

$4\ \textup{inches}$

Explanation:

If the radius is equal to 6 inches, then the diameter will be double that value, or 12 inches. One-third of 12 is 4, which is therefore the correct answer.

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Example Question #219 : Geometry

A right triangle has one leg with length $5\:cm$ and another leg with length $8\:cm$ . What is the length of the hypotenuse?

Possible Answers:

$\sqrt{89}$

10.5

$\sqrt{55}$

$\sqrt{67}$

Correct answer:

$\sqrt{89}$

Explanation:

Since we are dealing with a right triangle, we can use the Pythagorean Theorem:

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

where and are leg lengths of and , respectively, and is the length of the hypotenuse.

Substituting values into the Theorem:

$5^{2}+8^{2}=c^{2}$

$25+64=c^{2}$

$89=c^{2}$

$\sqrt{89}=c$

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Example Question #1 : How To Find Length Of A Line

Line has a length of $60\:cm$ . It is bisected at point , and the resulting segment is bisected again at point . What is the length of the line segment ?

Possible Answers:

$15\:cm$

$30\:cm$

$20\:cm$

$7.5\:cm$

$45\:cm$

Correct answer:

$15\:cm$

Explanation:

A line that is bisected is split into two segments of equal length. Therefore, if line is bisected at point ,

$AC=\frac{1}{2}AB=30\: cm$ .

Consequently, bisecting line segment at point :

$AD=\frac{1}{2}AC=\frac{1}{2}(30)=15\:cm$

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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 Area Of A Trapezoid

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

Example Question #213 : Geometry

Example Question #214 : Geometry

Example Question #2 : How To Find The Area Of A Trapezoid

Example Question #216 : Geometry

Example Question #1 : How To Find Length Of A Line

Example Question #218 : Geometry

Example Question #219 : Geometry

Example Question #1 : How To Find Length Of A Line

All SSAT Middle Level Math Resources

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