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SSAT Upper Level Math : Properties of Triangles

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 #11 : How To Find The Height Of An Acute / Obtuse Triangle

A triangle has an area of 64ft^2 and a base of 32ft . In feet, what is the height?

Possible Answers:

6ft

2ft

8ft

4ft

Correct answer:

4ft

Explanation:

Use the formula to find the area of a triangle.

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

Now, plug in the values for the area and the base to solve for height .

$64=\frac{32\times h}{2}$

128=32h

h=4

The height of the triangle is feet.

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Example Question #1 : How To Find The Area Of An Acute / Obtuse Triangle

Heron

Give the area of the above triangle.

Possible Answers:

675

450

900

1,125

800

Correct answer:

900

Explanation:

By Heron's formula, the area of a triangle given its sidelengths is

$A =\sqrt{ s (s-a) (s-b) (s-c)}$

Where a, b, c are the sidelengths and

$s = \frac{1}{2} (a+b+c)$ ,

or half the perimeter.

Setting a = 50, b = 45, c=85 ,

$s = \frac{1}{2} (a+b+c) = \frac{1}{2} (50+45+85) = 90$

Therefore,

$A =\sqrt{ s (s-a) (s-b) (s-c)}$

$A =\sqrt{90 (90 -50) (90 -45) (90 -85)}$

$A =\sqrt{90 \cdot 40 \cdot 45 \cdot 5 }$

$A =\sqrt{810,000 }$

A =900

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Example Question #2 : How To Find The Area Of An Acute / Obtuse Triangle

Heron

Give the area of the above triangle.

Possible Answers:

$60 \sqrt{7 }$

$30 \sqrt{ 14 }$

160

216

240

Correct answer:

$60 \sqrt{7 }$

Explanation:

By Heron's formula, the area of a triangle given its sidelengths is

$A =\sqrt{ s (s-a) (s-b) (s-c)}$ ,

where a, b, c are the sidelengths and

$s = \frac{1}{2} (a+b+c)$ ,

or half the perimeter.

Setting a = 16, b = 20, c=24 ,

$s = \frac{1}{2} (a+b+c) = \frac{1}{2} (16+20+24) = 30$ .

Therefore,

$A =\sqrt{ s (s-a) (s-b) (s-c)}$

$A =\sqrt{ 30 (30-16) (30-20) (30-24)}$

$A =\sqrt{ 30 \cdot 14 \cdot 10 \cdot 6 }$

$A = \sqrt{25,200 }$

$A = \sqrt{3,600 } \cdot\sqrt{7}$

$A = 60 \sqrt{7 }$

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Example Question #3 : How To Find The Area Of An Acute / Obtuse Triangle

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

Possible Answers:

120

Correct answer:

Explanation:

First, find the height of the triangle by listing out the multiples of .

8: 8, 16, 24, 32

Since is the only multiple of that is between and , it must be the height.

Now, find the area of the triangle.

$\text{Area}=\frac{5\times24}{2}=60$

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Example Question #2 : How To Find The Area Of An Acute / Obtuse Triangle

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

Possible Answers:

240

160

180

120

Correct answer:

120

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.

$\text{Area}=\frac{20\times 12}{2}=\frac{240}{2}=120$

The area of the triangle is 120 .

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Example Question #4 : How To Find The Area Of An Acute / Obtuse Triangle

The height of an acute triangle is , and the base is . What is the area of this triangle?

Possible Answers:

280

490

560

360

Correct answer:

280

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.

$\text{Area}=\frac{40\times14}{2}=\frac{560}{2}=280$

The area of the triangle is 280 .

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Example Question #4 : How To Find The Area Of An Acute / Obtuse Triangle

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

Possible Answers:

9t^2

20t^2

10t^2

Correct answer:

10t^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.

$\text{Area}=\frac{4t\times 5t}{2}=\frac{20t^2}{2}=10t^2$

The area of the triangle is 10t^2 .

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Example Question #5 : How To Find The Area Of An Acute / Obtuse Triangle

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

$\text{Area}=\frac{4\times20}{2}=\frac{80}{2}=40$

The area of the triangle is .

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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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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Properties of Triangles

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

All SSAT Upper Level Math Resources

Example Questions

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

Example Question #1 : How To Find The Area Of An Acute / Obtuse Triangle

Example Question #2 : How To Find The Area Of An Acute / Obtuse Triangle

Example Question #3 : How To Find The Area Of An Acute / Obtuse Triangle

Example Question #2 : How To Find The Area Of An Acute / Obtuse Triangle

Example Question #4 : How To Find The Area Of An Acute / Obtuse Triangle

Example Question #4 : How To Find The Area Of An Acute / Obtuse Triangle

Example Question #5 : How To Find The Area Of An Acute / Obtuse Triangle

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

All SSAT Upper Level Math Resources

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