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SSAT Elementary Level Math : Plane Geometry

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

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All SSAT Elementary Level Math Resources

12 Diagnostic Tests 526 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #591 : Geometry

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

Possible Answers:

Correct answer:

Explanation:

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

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

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

Possible Answers:

the height and base

the perimeter

two side lengths

its angles

Correct answer:

the height and base

Explanation:

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

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Example Question #591 : Plane Geometry

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:

4.5 $\displaystyle 4.5$

12.25 $\displaystyle 12.25$

$\displaystyle 9$

6.5 $\displaystyle 6.5$

Correct answer:

4.5 $\displaystyle 4.5$

Explanation:

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

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

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Example Question #5 : 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:

$\displaystyle 20$

$\displaystyle 12$

$\displaystyle 4$

$\displaystyle 6$

$\displaystyle 13$

Correct answer:

$\displaystyle 6$

Explanation:

The formula to find the area of a triangle is

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

First, we should multiply $\displaystyle 3$ (base) $\times$ $\displaystyle \times$ $\displaystyle 4$ (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 $\displaystyle 6$.

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Example Question #592 : Plane Geometry

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

Possible Answers:

$36\: cm^{2}$ $\displaystyle 36\: cm^{2}$

$12\: cm^{2}$ $\displaystyle 12\: cm^{2}$

$18\, cm^{2}$ $\displaystyle 18\, cm^{2}$

$72\: cm^{2}$ $\displaystyle 72\: cm^{2}$

Correct answer:

$36\: cm^{2}$ $\displaystyle 36\: cm^{2}$

Explanation:

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

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

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

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Example Question #593 : Plane Geometry

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

Possible Answers:

$\displaystyle 22$

$\displaystyle 56$

$\displaystyle 58$

112 $\displaystyle 112$

$\displaystyle 57$

Correct answer:

$\displaystyle 56$

Explanation:

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

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

Therefore the area of this triangle is $\displaystyle 56$.

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Example Question #595 : Geometry

Screen_shot_2014-01-06_at_12.34.19_pm

What is the area of the triangle?

Possible Answers:

Correct answer:

Explanation:

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

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

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Example Question #6 : How To Find The Area Of A Triangle

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

Possible Answers:

$16\;in^2$ $\displaystyle 16\;in^2$

$12\;in^{2}$ $\displaystyle 12\;in^{2}$

$32\;in^2$ $\displaystyle 32\;in^2$

$11\;in^2$ $\displaystyle 11\;in^2$

$24\;in^2$ $\displaystyle 24\;in^2$

Correct answer:

$12\;in^{2}$ $\displaystyle 12\;in^{2}$

Explanation:

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

Plug in the values given to solve the equation:

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

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

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Example Question #7 : How To Find The Area Of A Triangle

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

Possible Answers:

$120\ cm^{2}$ $\displaystyle 120\ cm^{2}$

$22\ cm^{2}$ $\displaystyle 22\ cm^{2}$

$60\ cm^{2}$ $\displaystyle 60\ cm^{2}$

$70\ cm^{2}$ $\displaystyle 70\ cm^{2}$

$72\ cm^{2}$ $\displaystyle 72\ cm^{2}$

Correct answer:

$60\ cm^{2}$ $\displaystyle 60\ cm^{2}$

Explanation:

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

Plug in the given values to solve for the area:

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

= $5cm\times12cm$ $\displaystyle 5cm\times12cm$

= 60cm^2 $\displaystyle 60cm^2$

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

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Example Question #11 : How To Find The Area Of A Triangle

What is the area of a right triangle with a base of length 4 and a height that is 3 times longer than the base?

Possible Answers:

$\displaystyle 24$

$\displaystyle 48$

$\displaystyle 36$

$\displaystyle 12$

$\displaystyle 6$

Correct answer:

$\displaystyle 24$

Explanation:

The area of a triangle is given by the formula $A = \frac{1}{2}\times b \times h$ $\displaystyle A = \frac{1}{2}\times b \times h$, where $\displaystyle b$ is the length of the base and $\displaystyle h$ is the height.

First let's figure out the height. The base is 4, and the height is 3 times greater than the base:

$3 \times 4 = 12$ $\displaystyle 3 \times 4 = 12$

Now plug the base and height into the area formula:

$A = 0.5 \times 4 \times 12 = 2 \times 12 = 24$ $\displaystyle A = 0.5 \times 4 \times 12 = 2 \times 12 = 24$

The area of the triangle is 24.

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SSAT Elementary Level Math : Plane Geometry

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

All SSAT Elementary Level Math Resources

Example Questions

Example Question #591 : Geometry

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

Example Question #591 : Plane Geometry

Example Question #5 : How To Find The Area Of A Triangle

Example Question #592 : Plane Geometry

Example Question #593 : Plane Geometry

Example Question #595 : Geometry

Example Question #6 : How To Find The Area Of A Triangle

Example Question #7 : How To Find The Area Of A Triangle

Example Question #11 : How To Find The Area Of A Triangle

All SSAT Elementary Level Math Resources

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