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Common Core: 6th Grade Math : Find Area of Polygons: CCSS.Math.Content.6.G.A.1

Study concepts, example questions & explanations for Common Core: 6th Grade Math

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All Common Core: 6th Grade Math Resources

6 Diagnostic Tests 186 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #57 : How To Find The Area Of A Triangle

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

Possible Answers:

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

$66\textup{ in}^2$ $\displaystyle 66\textup{ in}^2$

$63.5\textup{ in}^2$ $\displaystyle 63.5\textup{ in}^2$

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

$74.5\textup{ in}^2$ $\displaystyle 74.5\textup{ in}^2$

Correct answer:

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

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:

3 3

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.

$A=16\times 9$ $\displaystyle A=16\times 9$

A=144 $\displaystyle A=144$

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 $\displaystyle 2$.

$144\div 2= 72\textup{ in}^2$ $\displaystyle 144\div 2= 72\textup{ in}^2$

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 #51 : How To Find The Area Of A Triangle

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

Possible Answers:

$64\textup{ in}^2$ $\displaystyle 64\textup{ in}^2$

$66\textup{ in}^2$ $\displaystyle 66\textup{ in}^2$

$62.5\textup{ in}^2$ $\displaystyle 62.5\textup{ in}^2$

$58.5\textup{ in}^2$ $\displaystyle 58.5\textup{ in}^2$

$60\textup{ in}^2$ $\displaystyle 60\textup{ in}^2$

Correct answer:

$64\textup{ in}^2$ $\displaystyle 64\textup{ in}^2$

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:

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

Substitute in our side lengths.

$A=16\times 8$ $\displaystyle A=16\times 8$

A=128 $\displaystyle A=128$

$128\div 2= 64\textup{ in}^2$ $\displaystyle 128\div 2= 64\textup{ in}^2$

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 #742 : Geometry

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

Possible Answers:

$105.5\textup{ in}^2$ $\displaystyle 105.5\textup{ in}^2$

$104\textup{ in}^2$ $\displaystyle 104\textup{ in}^2$

$101.5\textup{ in}^2$ $\displaystyle 101.5\textup{ in}^2$

$102\textup{ in}^2$ $\displaystyle 102\textup{ in}^2$

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

Correct answer:

$102\textup{ in}^2$ $\displaystyle 102\textup{ in}^2$

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.

$A=17\times 12$ $\displaystyle A=17\times 12$

A=204 $\displaystyle A=204$

$204\div 2= 102\textup{ in}^2$ $\displaystyle 204\div 2= 102\textup{ in}^2$

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 #743 : Geometry

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

Possible Answers:

$95\textup{ in}^2$ $\displaystyle 95\textup{ in}^2$

$91.5\textup{ in}^2$ $\displaystyle 91.5\textup{ in}^2$

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

$90.5\textup{ in}^2$ $\displaystyle 90.5\textup{ in}^2$

$93.5\textup{ in}^2$ $\displaystyle 93.5\textup{ in}^2$

Correct answer:

$93.5\textup{ in}^2$ $\displaystyle 93.5\textup{ in}^2$

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.

$A=17\times 11$ $\displaystyle A=17\times 11$

A=187 $\displaystyle A=187$

$187\div 2= 93.5\textup{ in}^2$ $\displaystyle 187\div 2= 93.5\textup{ in}^2$

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 #744 : Geometry

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

Possible Answers:

$87.5\textup{ in}^2$ $\displaystyle 87.5\textup{ in}^2$

$81\textup{ in}^2$ $\displaystyle 81\textup{ in}^2$

$83.5\textup{ in}^2$ $\displaystyle 83.5\textup{ in}^2$

$89\textup{ in}^2$ $\displaystyle 89\textup{ in}^2$

$85\textup{ in}^2$ $\displaystyle 85\textup{ in}^2$

Correct answer:

$85\textup{ in}^2$ $\displaystyle 85\textup{ in}^2$

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:

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

Substitute in our side lengths.

$A=17\times 10$ $\displaystyle A=17\times 10$

A=170 $\displaystyle A=170$

$170\div 2= 85\textup{ in}^2$ $\displaystyle 170\div 2= 85\textup{ in}^2$

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 #61 : How To Find The Area Of A Triangle

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

Possible Answers:

$74\textup{ in}^2$ $\displaystyle 74\textup{ in}^2$

$78.5\textup{ in}^2$ $\displaystyle 78.5\textup{ in}^2$

$76.5\textup{ in}^2$ $\displaystyle 76.5\textup{ in}^2$

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

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

Correct answer:

$76.5\textup{ in}^2$ $\displaystyle 76.5\textup{ in}^2$

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:

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

Substitute in our side lengths.

$A=17\times 9$ $\displaystyle A=17\times 9$

A=153 $\displaystyle A=153$

$153\div 2= 76.5\textup{ in}^2$ $\displaystyle 153\div 2= 76.5\textup{ in}^2$

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 #746 : Geometry

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

Possible Answers:

$114\textup{ in}^2$ $\displaystyle 114\textup{ in}^2$

$117.5\textup{ in}^2$ $\displaystyle 117.5\textup{ in}^2$

$117\textup{ in}^2$ $\displaystyle 117\textup{ in}^2$

$114.5\textup{ in}^2$ $\displaystyle 114.5\textup{ in}^2$

$119\textup{ in}^2$ $\displaystyle 119\textup{ in}^2$

Correct answer:

$117\textup{ in}^2$ $\displaystyle 117\textup{ in}^2$

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.

$A=18\times 13$ $\displaystyle A=18\times 13$

A=234 $\displaystyle A=234$

$234\div 2= 117\textup{ in}^2$ $\displaystyle 234\div 2= 117\textup{ in}^2$

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 #747 : Geometry

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

Possible Answers:

$104\textup{ in}^2$ $\displaystyle 104\textup{ in}^2$

$108\textup{ in}^2$ $\displaystyle 108\textup{ in}^2$

$102.5\textup{ in}^2$ $\displaystyle 102.5\textup{ in}^2$

$106\textup{ in}^2$ $\displaystyle 106\textup{ in}^2$

$105.5\textup{ in}^2$ $\displaystyle 105.5\textup{ in}^2$

Correct answer:

$108\textup{ in}^2$ $\displaystyle 108\textup{ in}^2$

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.

$A=18\times 12$ $\displaystyle A=18\times 12$

A=216 $\displaystyle A=216$

$216\div 2= 108\textup{ in}^2$ $\displaystyle 216\div 2= 108\textup{ in}^2$

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 #748 : Geometry

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

Possible Answers:

$99\textup{ in}^2$ $\displaystyle 99\textup{ in}^2$

$105\textup{ in}^2$ $\displaystyle 105\textup{ in}^2$

$104.5\textup{ in}^2$ $\displaystyle 104.5\textup{ in}^2$

$98.5\textup{ in}^2$ $\displaystyle 98.5\textup{ in}^2$

$103\textup{ in}^2$ $\displaystyle 103\textup{ in}^2$

Correct answer:

$99\textup{ in}^2$ $\displaystyle 99\textup{ in}^2$

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:

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

Substitute in our side lengths.

$A=18\times 11$ $\displaystyle A=18\times 11$

A=198 $\displaystyle A=198$

$198\div 2= 99\textup{ in}^2$ $\displaystyle 198\div 2= 99\textup{ in}^2$

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 #61 : How To Find The Area Of A Triangle

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

Possible Answers:

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

$88\textup{ in}^2$ $\displaystyle 88\textup{ in}^2$

$85.5\textup{ in}^2$ $\displaystyle 85.5\textup{ in}^2$

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

$84.5\textup{ in}^2$ $\displaystyle 84.5\textup{ in}^2$

Correct answer:

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

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:

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

Substitute in our side lengths.

$A=18\times 10$ $\displaystyle A=18\times 10$

A=180 $\displaystyle A=180$

$180\div 2= 90\textup{ in}^2$ $\displaystyle 180\div 2= 90\textup{ in}^2$

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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Common Core: 6th Grade Math : Find Area of Polygons: CCSS.Math.Content.6.G.A.1

Study concepts, example questions & explanations for Common Core: 6th Grade Math

All Common Core: 6th Grade Math Resources

Example Questions

Example Question #57 : How To Find The Area Of A Triangle

Example Question #51 : How To Find The Area Of A Triangle

Example Question #742 : Geometry

Example Question #743 : Geometry

Example Question #744 : Geometry

Example Question #61 : How To Find The Area Of A Triangle

Example Question #746 : Geometry

Example Question #747 : Geometry

Example Question #748 : Geometry

Example Question #61 : How To Find The Area Of A Triangle

All Common Core: 6th Grade Math Resources

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