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ISEE Lower Level Quantitative : How to find the area of a triangle

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

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All ISEE Lower Level Quantitative Resources

20 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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Example Question #41 : Triangles

What is the area of a triangle with a base of 8 and a height of 3?

Possible Answers:

Correct answer:

Explanation:

The area of a triangle is $\frac{1}{2}*(base* height)$ . We know that our base is 8 and our height is 3.

In this case, the equation is $\frac{1}{2}*(8* 3)$ . Now we can solve this equation.

$\frac{1}{2}(24)$

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

What is the area of a triangle that has a base of 7 and a height of 10?

Possible Answers:

Correct answer:

Explanation:

To find the area of a triangle, we use $\frac{1}{2}*(base* height)$ . We know the height of the triangle is 10 and the base is 7.

$\frac{1}{2}*(base*height)=\frac{1}{2}*(7*10)$

$\frac{1}{2}*(70)$

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

What is the area of a triangle with a base of 7cm and a height of 4cm?

Possible Answers:

28cm^2

21cm^2

11cm^2

14cm^2

Correct answer:

14cm^2

Explanation:

Use the formula for the area of a triangle

$\frac{1}{2}bh$

to solve this problem. Plug in and you get $14\ cm^{2}$ .

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

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

Possible Answers:

$24 ft^{2}$

$8ft^{2}$

$6ft^{2}$

$48ft^{2}$

Correct answer:

$24 ft^{2}$

Explanation:

The formula for finding the area of a triangle is $\frac{1}{2}(base\times height)$ . Multiply the base times the height first. $8\times6=48$ . Then, either multiply $\frac{1}{2}\times\frac{48}{1}$ , or simply divide $48\div2$ . Therefore the answer is $24ft^{2}$ .

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

A right triangle has a base of 4 and a height of 7.

What is the triangle's area?

Possible Answers:

Correct answer:

Explanation:

An area of a triangle is

$\frac{1}{2}\times base\times height$

In this case

$\frac{1}{2}\times 4\times 7=14$

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

If the base of a triangle is 12 cm, and the height of the triangle is 4 cm, what is the total area of the triangle?

Possible Answers:

$48\ cm^2$

$96\ cm^2$

$36\ cm^2$

$16\ cm^2$

$24\ cm^2$

Correct answer:

$24\ cm^2$

Explanation:

First, you must remember the formula for the area of a triangle $(A=\frac{1}{2}bh)$ .

Plug in the given values: $A=\frac{1}{2}(4)(12)$ .

Multiply to get 24. Since this is area, the units must be sqaured. Therefore, your final answer is $24\ cm^2$ .

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Example Question #1 : Find Area Of Polygons: Ccss.Math.Content.6.G.A.1

What is the area of the right triangle in the following figure?

Possible Answers:

$117\textup{ in}^2$

$81.5\textup{ in}^2$

$65.5\textup{ in}^2$

$58.5\textup{ in}^2$

$80\textup{ in}^2$

Correct answer:

$58.5\textup{ in}^2$

Explanation:

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

1 1

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=13\times 9$

A=117

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$117\div 2= 58.5\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

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Example Question #2 : Find Area Of Polygons: Ccss.Math.Content.6.G.A.1

What is the area of the right triangle in the following figure?

Possible Answers:

$48\textup{ in}^2$

$30\textup{ in}^2$

$36.5\textup{ in}^2$

$45.5\textup{ in}^2$

$42\textup{ in}^2$

Correct answer:

$48\textup{ in}^2$

Explanation:

First, let's transform the triangle into a rectangle:

2 1

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=12\times 8$

A=96

$96\div 2= 48\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

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Example Question #3 : Find Area Of Polygons: Ccss.Math.Content.6.G.A.1

What is the area of the right triangle in the following figure?

Possible Answers:

$52.5\textup{ in}^2$

$49.5\textup{ in}^2$

$60\textup{ in}^2$

$63\textup{ in}^2$

$58.5\textup{ in}^2$

Correct answer:

$49.5\textup{ in}^2$

Explanation:

First, let's transform the triangle into a rectangle:

3 3

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=11\times 9$

A=99

$99\div 2= 49.5\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

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Example Question #1 : Find Area Of Polygons: Ccss.Math.Content.6.G.A.1

What is the area of the right triangle in the following figure?

Possible Answers:

$40.5\textup{ in}^2$

$43\textup{ in}^2$

$42\textup{ in}^2$

$30.5\textup{ in}^2$

$35\textup{ in}^2$

Correct answer:

$35\textup{ in}^2$

Explanation:

First, let's transform the triangle into a rectangle:

4 4

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=10\times 7$

A=70

$70\div 2= 35\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

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All ISEE Lower Level Quantitative Resources

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ISEE Lower Level Quantitative : How to find the area of a triangle

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

All ISEE Lower Level Quantitative Resources

Example Questions

Example Question #41 : Triangles

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

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

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

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

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

Example Question #1 : Find Area Of Polygons: Ccss.Math.Content.6.G.A.1

Example Question #2 : Find Area Of Polygons: Ccss.Math.Content.6.G.A.1

Example Question #3 : Find Area Of Polygons: Ccss.Math.Content.6.G.A.1

Example Question #1 : Find Area Of Polygons: Ccss.Math.Content.6.G.A.1

All ISEE Lower Level Quantitative Resources

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