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SSAT Upper Level Math : Geometry

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

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #6 : How To Find The Area Of An Acute / Obtuse Triangle

The height of a triangle is , and the base is . In terms of , what is the area of the triangle?

Possible Answers:

48a^2

36a^2

24a^2

14a

Correct answer:

24a^2

Explanation:

Use the following formula to find the area of a triangle:

$\text{Area}=\frac{base\times height}{2}$

Now, substitute in for the base and for the height.

$\text{Area}=\frac{6a\times8a}{2}=\frac{48a^2}{2}=24a^2$

The area of the triangle is 24a^2 .

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Example Question #7 : How To Find The Area Of An Acute / Obtuse Triangle

The height of a triangle is , and the base of the triangle is . In terms of , what is the area of the triangle?

Possible Answers:

54y^2

27y^2

36y^2

15y

Correct answer:

27y^2

Explanation:

Use the following formula to find the area of a triangle:

$\text{Area}=\frac{base\times height}{2}$

Now, substitute in for the base and for the height.

$\text{Area}=\frac{9y\times6y}{2}=\frac{54y^2}{2}=27y^2$

The area of the triangle is 27y^2 .

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Example Question #8 : How To Find The Area Of An Acute / Obtuse Triangle

The height of a triangle is , and the base is . What is the area of the triangle?

Possible Answers:

Correct answer:

Explanation:

Use the following formula to find the area of a triangle:

$\text{Area}=\frac{base\times height}{2}$

Now, substitute in for the base and for the height.

$\text{Area}=\frac{4\times14}{2}=\frac{56}{2}=28$

The area of the triangle is .

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Example Question #11 : How To Find The Area Of An Acute / Obtuse Triangle

The height of a triangle is 10g , and the base is . In terms of , what is the area of the triangle?

Possible Answers:

22g

60g^2

40g^2

30g^2

Correct answer:

30g^2

Explanation:

Use the following formula to find the area of a triangle:

$\text{Area}=\frac{base\times height}{2}$

Now, substitute in for the base and 10g for the height.

$\text{Area}=\frac{6g\times10g}{2}=\frac{60g^2}{2}=30g^2$

The area of the triangle is 30g^2 .

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Example Question #82 : Acute / Obtuse Triangles

The base of a triangle is inches, and the height of the triangle is inches. In terms of , what is the area of the triangle?

Possible Answers:

$\frac{y}{2}$ in^2

in^2

Correct answer:

in^2

Explanation:

Find the area of the triangle by using the formula $\frac{base\times height}{2}$ .

Now, substitute in for the base and for the height.

$\text{Area}=\frac{y\times8}{2}=\frac{8y}{2}=4y$

Don't forget to include the units, in^2

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Example Question #173 : Properties Of Triangles

The base of a triangle is 12x , and the height of the triangle is . If the area of the triangle is 120 , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Use the following formula to find the area of a triangle:

$\text{Area}=\frac{base\times height}{2}$

Now, substitute in 12x for the base, for the height, and 120 for the area..

Use algebraic opertions to solve for x.

$120=\frac{12x\times5}{2}$

60x=120

x=4

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Example Question #174 : Properties Of Triangles

The height of the triangle is , and the base of the triangle is . If the area of the triangle is , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Use the formula for the area of a triangle.

$\text{Area}=\frac{base \times height}{2}$

Substitute in for height, for the base, and for the area.

From here, use algebraic operations to isolate d on one side and all other numbers on the other side.

$80=\frac{5d\times 8}{2}$

40d=160

d=4

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Example Question #491 : Grade 8

A car dealership wants to fill a large spherical advertising ballon with helium. It can afford to buy 1,000 cubic yards of helium to fill this balloon. What is the greatest possible diameter of that balloon (nearest tenth of a yard)?

Possible Answers:

$7.7 \;\textrm{yd}$

$9.3 \;\textrm{yd}$

$6.2 \;\textrm{yd}$

$15.4 \;\textrm{yd}$

$12.4 \;\textrm{yd}$

Correct answer:

$12.4 \;\textrm{yd}$

Explanation:

The volume of a sphere, given its radius, is

$V = \frac{4\pi r^{3}}{3}$

Set V = 1,000 , solve for , and double that to get the diameter.

$1,000= \frac{4\pi r^{3}}{3}$

$r^{3} = \frac{1,000 \cdot 3 }{4\pi} \approx 238.7$

$r \approx \sqrt[3]{238.7} \approx 6.2$

The diameter is twice this, or 12.4 yards.

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Example Question #492 : Grade 8

The diameter of a sphere is . Give the volume of the sphere in terms of .

Possible Answers:

$72\pi t^3$

$10\pi t^3$

$30\pi t^3$

$36\pi t^3$

$24\pi t^3$

Correct answer:

$36\pi t^3$

Explanation:

The diameter of a sphere is so the radius of the sphere would be $6t\div 2=3t$

The volume enclosed by a sphere is given by the formula:

$Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\pi \times (3t)^3=\frac{4}{3}\pi\times 27t^3\Rightarrow Volume=36\pi t^3$

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Example Question #493 : Grade 8

A spherical balloon has a diameter of 10 meters. Give the volume of the balloon.

Possible Answers:

1000m^3

500m^3

523.6m^3

1023.3m^3

723.3m^3

Correct answer:

523.6m^3

Explanation:

The volume enclosed by a sphere is given by the formula:

$Volume=\frac{4}{3}\pi r^3$

where is the radius of the sphere. The diameter of the balloon is 10 meters so the radius of the sphere would be $10\div 2=5$ meters. Now we can get:

$Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\pi\times 5^3=\frac{4}{3}\times \pi \times 125\approx 523.6 m^3$

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SSAT Upper Level Math : Geometry

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #6 : How To Find The Area Of An Acute / Obtuse Triangle

Example Question #7 : How To Find The Area Of An Acute / Obtuse Triangle

Example Question #8 : How To Find The Area Of An Acute / Obtuse Triangle

Example Question #11 : How To Find The Area Of An Acute / Obtuse Triangle

Example Question #82 : Acute / Obtuse Triangles

Example Question #173 : Properties Of Triangles

Example Question #174 : Properties Of Triangles

Example Question #491 : Grade 8

Example Question #492 : Grade 8

Example Question #493 : Grade 8

All SSAT Upper Level Math Resources

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