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

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Example Questions

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

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

Possible Answers:

$27\textup{ in}^2$ $\displaystyle 27\textup{ in}^2$

$30\textup{ in}^2$ $\displaystyle 30\textup{ in}^2$

$22\textup{ in}^2$ $\displaystyle 22\textup{ in}^2$

$32.5\textup{ in}^2$ $\displaystyle 32.5\textup{ in}^2$

$26.5\textup{ in}^2$ $\displaystyle 26.5\textup{ in}^2$

Correct answer:

$27\textup{ in}^2$ $\displaystyle 27\textup{ in}^2$

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:

5 5

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

$A=l\times w$ $\displaystyle A=l\times w$

Substitute in our side lengths.

$A=9\times 6$ $\displaystyle A=9\times 6$

A=54 $\displaystyle A=54$

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 $\displaystyle 2$.

$54\div 2= 27\textup{ in}^2$ $\displaystyle 54\div 2= 27\textup{ in}^2$

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

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

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Example Question #4 : 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:

$40\textup{ in}^2$ $\displaystyle 40\textup{ in}^2$

$31.5\textup{ in}^2$ $\displaystyle 31.5\textup{ in}^2$

$36\textup{ in}^2$ $\displaystyle 36\textup{ in}^2$

$20\textup{ in}^2$ $\displaystyle 20\textup{ in}^2$

$22\textup{ in}^2$ $\displaystyle 22\textup{ in}^2$

Correct answer:

$20\textup{ in}^2$ $\displaystyle 20\textup{ in}^2$

Explanation:

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

6 6

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

$A=l\times w$ $\displaystyle A=l\times w$

Substitute in our side lengths.

$A=8\times 5$ $\displaystyle A=8\times 5$

A=40 $\displaystyle A=40$

$40\div 2= 20\textup{ in}^2$ $\displaystyle 40\div 2= 20\textup{ in}^2$

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

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

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Example Question #12 : How To Find The Area Of A Triangle

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

Possible Answers:

$14\textup{ in}^2$ $\displaystyle 14\textup{ in}^2$

$10.5\textup{ in}^2$ $\displaystyle 10.5\textup{ in}^2$

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

$13\textup{ in}^2$ $\displaystyle 13\textup{ in}^2$

$12.5\textup{ in}^2$ $\displaystyle 12.5\textup{ in}^2$

Correct answer:

$14\textup{ in}^2$ $\displaystyle 14\textup{ in}^2$

Explanation:

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

7 7

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

$A=l\times w$ $\displaystyle A=l\times w$

Substitute in our side lengths.

$A=7\times 4$ $\displaystyle A=7\times 4$

A=28 $\displaystyle A=28$

$28\div 2= 14\textup{ in}^2$ $\displaystyle 28\div 2= 14\textup{ in}^2$

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

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

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Example Question #13 : How To Find The Area Of A Triangle

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

Possible Answers:

$70\textup{ in}^2$ $\displaystyle 70\textup{ in}^2$

$72.5\textup{ in}^2$ $\displaystyle 72.5\textup{ in}^2$

$80\textup{ in}^2$ $\displaystyle 80\textup{ in}^2$

$75\textup{ in}^2$ $\displaystyle 75\textup{ in}^2$

$68\textup{ in}^2$ $\displaystyle 68\textup{ in}^2$

Correct answer:

$70\textup{ in}^2$ $\displaystyle 70\textup{ in}^2$

Explanation:

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

8 8

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

$A=l\times w$ $\displaystyle A=l\times w$

Substitute in our side lengths.

$A=14\times 10$ $\displaystyle A=14\times 10$

A=140 $\displaystyle A=140$

$140\div 2= 70\textup{ in}^2$ $\displaystyle 140\div 2= 70\textup{ in}^2$

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

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

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Example Question #8 : 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:

$86.5\textup{ in}^2$ $\displaystyle 86.5\textup{ in}^2$

$72\textup{ in}^2$ $\displaystyle 72\textup{ in}^2$

$80\textup{ in}^2$ $\displaystyle 80\textup{ in}^2$

$73.5\textup{ in}^2$ $\displaystyle 73.5\textup{ in}^2$

$82.5\textup{ in}^2$ $\displaystyle 82.5\textup{ in}^2$

Correct answer:

$82.5\textup{ in}^2$ $\displaystyle 82.5\textup{ in}^2$

Explanation:

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

9 9

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

$A=l\times w$ $\displaystyle A=l\times w$

Substitute in our side lengths.

$A=15\times 11$ $\displaystyle A=15\times 11$

A=165 $\displaystyle A=165$

$165\div 2= 82.5\textup{ in}^2$ $\displaystyle 165\div 2= 82.5\textup{ in}^2$

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

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

Report an Error

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:

$96\textup{ in}^2$ $\displaystyle 96\textup{ in}^2$

$98\textup{ in}^2$ $\displaystyle 98\textup{ in}^2$

$90\textup{ in}^2$ $\displaystyle 90\textup{ in}^2$

$99.5\textup{ in}^2$ $\displaystyle 99.5\textup{ in}^2$

$94.5\textup{ in}^2$ $\displaystyle 94.5\textup{ in}^2$

Correct answer:

$96\textup{ in}^2$ $\displaystyle 96\textup{ in}^2$

Explanation:

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

10 1

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

$A=l\times w$ $\displaystyle A=l\times w$

Substitute in our side lengths.

$A=16\times 12$ $\displaystyle A=16\times 12$

A=192 $\displaystyle A=192$

$192\div 2= 96\textup{ in}^2$ $\displaystyle 192\div 2= 96\textup{ in}^2$

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

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

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Example Question #1173 : Grade 6

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

Possible Answers:

$97\textup{ in}^2$ $\displaystyle 97\textup{ in}^2$

$100\textup{ in}^2$ $\displaystyle 100\textup{ in}^2$

$110.5\textup{ in}^2$ $\displaystyle 110.5\textup{ in}^2$

$115.5\textup{ in}^2$ $\displaystyle 115.5\textup{ in}^2$

$113.5\textup{ in}^2$ $\displaystyle 113.5\textup{ in}^2$

Correct answer:

$110.5\textup{ in}^2$ $\displaystyle 110.5\textup{ in}^2$

Explanation:

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

11 1

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

$A=l\times w$ $\displaystyle A=l\times w$

Substitute in our side lengths.

$A=17\times 13$ $\displaystyle A=17\times 13$

A=221 $\displaystyle A=221$

$221\div 2= 110.5\textup{ in}^2$ $\displaystyle 221\div 2= 110.5\textup{ in}^2$

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

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

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Example Question #11 : Geometry

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

Possible Answers:

$120.5\textup{ in}^2$ $\displaystyle 120.5\textup{ in}^2$

$126\textup{ in}^2$ $\displaystyle 126\textup{ in}^2$

$124\textup{ in}^2$ $\displaystyle 124\textup{ in}^2$

$116\textup{ in}^2$ $\displaystyle 116\textup{ in}^2$

$118.5\textup{ in}^2$ $\displaystyle 118.5\textup{ in}^2$

Correct answer:

$126\textup{ in}^2$ $\displaystyle 126\textup{ in}^2$

Explanation:

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

12 1

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

$A=l\times w$ $\displaystyle A=l\times w$

Substitute in our side lengths.

$A=18\times 14$ $\displaystyle A=18\times 14$

A=252 $\displaystyle A=252$

$252\div 2= 126\textup{ in}^2$ $\displaystyle 252\div 2= 126\textup{ in}^2$

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

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

Report an Error

Example Question #11 : 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:

$57.5\textup{ in}^2$ $\displaystyle 57.5\textup{ in}^2$

$58\textup{ in}^2$ $\displaystyle 58\textup{ in}^2$

$52\textup{ in}^2$ $\displaystyle 52\textup{ in}^2$

$55\textup{ in}^2$ $\displaystyle 55\textup{ in}^2$

$56.5\textup{ in}^2$ $\displaystyle 56.5\textup{ in}^2$

Correct answer:

$52\textup{ in}^2$ $\displaystyle 52\textup{ in}^2$

Explanation:

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:

$A=l\times w$ $\displaystyle A=l\times w$

Substitute in our side lengths.

$A=13\times 8$ $\displaystyle A=13\times 8$

A=104 $\displaystyle A=104$

$104\div 2= 52\textup{ in}^2$ $\displaystyle 104\div 2= 52\textup{ in}^2$

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

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

Report an Error

Example Question #13 : Geometry

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

Possible Answers:

$48\textup{ in}^2$ $\displaystyle 48\textup{ in}^2$

$49.5\textup{ in}^2$ $\displaystyle 49.5\textup{ in}^2$

$45.5\textup{ in}^2$ $\displaystyle 45.5\textup{ in}^2$

$47\textup{ in}^2$ $\displaystyle 47\textup{ in}^2$

$46.5\textup{ in}^2$ $\displaystyle 46.5\textup{ in}^2$

Correct answer:

$45.5\textup{ in}^2$ $\displaystyle 45.5\textup{ in}^2$

Explanation:

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

2 2

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

$A=l\times w$ $\displaystyle A=l\times w$

Substitute in our side lengths.

$A=13\times 7$ $\displaystyle A=13\times 7$

A=91 $\displaystyle A=91$

$91\div 2= 45.5\textup{ in}^2$ $\displaystyle 91\div 2= 45.5\textup{ in}^2$

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

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

Report an Error

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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 #11 : How To Find The Area Of A Triangle

Example Question #4 : Find Area Of Polygons: Ccss.Math.Content.6.G.A.1

Example Question #12 : How To Find The Area Of A Triangle

Example Question #13 : How To Find The Area Of A Triangle

Example Question #8 : 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 #1173 : Grade 6

Example Question #11 : Geometry

Example Question #11 : Find Area Of Polygons: Ccss.Math.Content.6.G.A.1

Example Question #13 : Geometry

All ISEE Lower Level Quantitative Resources

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