SSAT Elementary Level Math : How to find the area of a triangle

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

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Example Questions

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

The altitude of a triangle is given as \displaystyle a = 10, and its base as \displaystyle 3a. What is the area of the triangle? 

Possible Answers:

\displaystyle 40

\displaystyle 400

\displaystyle 150

\displaystyle 200

\displaystyle 300

Correct answer:

\displaystyle 150

Explanation:

The area of a triangle is given by \displaystyle 0.5\times altitude\times base.

altitude \displaystyle = 10

base \displaystyle = 3\times a = \displaystyle 30

Therefore:

Area \displaystyle = 0.5\times10\times30 = 150

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

What is the area of a triangle with a base of 11 and a height of 4?

Possible Answers:

44

60

6

22

14

Correct answer:

22

Explanation:

The formula to find the area of a triangle is \displaystyle \frac{base \cdot height}{2}. First, we should multiply 11 (base) x 4 (height), to get a total of 44. Next, we need to divide 44 by 2, which gives us a total area of 22.

Example Question #592 : Plane Geometry

You can find the area of a triangle if you know ___________.

Possible Answers:

the perimeter

its angles

the height and base

two side lengths

Correct answer:

the height and base

Explanation:

\displaystyle Area _{\Delta } = \frac{1}{2}\times base \times height

Example Question #1 : Triangles

Squareslice

The square shown above has a side length of 3 and is divided into two triangles by its diagonal. What is the area of one of the triangles?

Possible Answers:

\displaystyle 6.5

\displaystyle 4.5

\displaystyle 12.25

\displaystyle 9

Correct answer:

\displaystyle 4.5

Explanation:

The area of the square is side times side, \displaystyle 3\times3=9.

Each triangle is half of the square, \displaystyle 9\div2=4.5.

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

Screen_shot_2014-01-10_at_1.07.49_pm

What is the area of the triangle?

Possible Answers:

\displaystyle 13

\displaystyle 4

\displaystyle 20

\displaystyle 12

\displaystyle 6

Correct answer:

\displaystyle 6

Explanation:

The formula to find the area of a triangle is 

\displaystyle \frac{base \times height}{2}

First, we should multiply \displaystyle 3 (base) \displaystyle \times \displaystyle 4 (height), to get a total of \displaystyle 12.

Next, we need to divide \displaystyle 12 by \displaystyle 2, which gives us a total area of \displaystyle 6

Example Question #2 : Triangles

An isosceles triangle has a base of 12 cm and a height of 6 cm. What is the area of the triangle?

Possible Answers:

\displaystyle 72\: cm^{2}

\displaystyle 12\: cm^{2}

\displaystyle 18\, cm^{2}

\displaystyle 36\: cm^{2}

Correct answer:

\displaystyle 36\: cm^{2}

Explanation:

To find the area of a triangle, you must multiply \displaystyle \frac{1}{2} by the base (12 cm) by the height (6 cm):

\displaystyle \frac{12\: cm}{2}\times6 \: cm=36\: cm^{2}

Therefore the area of this triangle is \displaystyle 36\: cm^{2}.

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

A triangle has a base of 14 and a height of 8. What is the area of the triangle?

Possible Answers:

\displaystyle 112

\displaystyle 58

\displaystyle 57

\displaystyle 56

\displaystyle 22

Correct answer:

\displaystyle 56

Explanation:

To find the area of a triangle, multiply the base (14) by the height (8) and divide by 2:

\displaystyle \frac{14}{2}\times8=56

Therefore the area of this triangle is \displaystyle 56.

 

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

Screen_shot_2014-01-06_at_12.34.19_pm

What is the area of the triangle?

Possible Answers:

28

24

60

30

48

Correct answer:

24

Explanation:

The formula to find the area of a triangle is \displaystyle \frac{base \times height}{2}.

\displaystyle A = \frac{6\times 8}{2}=24

Example Question #1 : Triangles

If a triangle has a base of 3 inches and a height of 8 inches, what is the area of the triangle?

Possible Answers:

\displaystyle 32\;in^2

\displaystyle 24\;in^2

\displaystyle 11\;in^2

\displaystyle 12\;in^{2}

\displaystyle 16\;in^2

 

 

Correct answer:

\displaystyle 12\;in^{2}

Explanation:

The formula for the area of a triangle is  \displaystyle \frac{1}{2} \times base \times height= area.

Plug in the values given to solve the equation:  

\displaystyle \frac{1}{2}(3\;in)(8\;in)= 

 

\displaystyle \frac{1}{2}\times 3\;in \times 8\;in = \frac{1}{2}\;\times24\;in^{2}=12\;in^2

 

Example Question #2 : Triangles

A triangle has a base of 10 centimeters and a height of 12 centimeters. What is the area of the triangle?

Possible Answers:

\displaystyle 72\ cm^{2}

\displaystyle 60\ cm^{2}

 

\displaystyle 22\ cm^{2}

\displaystyle 70\ cm^{2}

\displaystyle 120\ cm^{2}

Correct answer:

\displaystyle 60\ cm^{2}

 

Explanation:

The formula for the area of a triangle is \displaystyle area=\frac{1}{2}(base)(height).

Plug in the given values to solve for the area:

\displaystyle \frac{1}{2}\times10cm\times12cm

 = \displaystyle 5cm\times12cm

 = \displaystyle 60cm^2 

The area of this triangle is \displaystyle 60cm^{2}.

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