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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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Example Questions

Example Question #1 : Geometry

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

Possible Answers:

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

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

$81.5\textup{ in}^2$ $\displaystyle 81.5\textup{ in}^2$

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

$65.5\textup{ in}^2$ $\displaystyle 65.5\textup{ in}^2$

Correct answer:

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

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:

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

Substitute in our side lengths.

$A=13\times 9$ $\displaystyle A=13\times 9$

A=117 $\displaystyle A=117$

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 $\displaystyle 2$.

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

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

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

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Example Question #2 : Geometry

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

Possible Answers:

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

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

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

$42\textup{ in}^2$ $\displaystyle 42\textup{ in}^2$

$36.5\textup{ in}^2$ $\displaystyle 36.5\textup{ in}^2$

Correct answer:

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

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:

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

Substitute in our side lengths.

$A=12\times 8$ $\displaystyle A=12\times 8$

A=96 $\displaystyle A=96$

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

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

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

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Example Question #1 : Geometry

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

Possible Answers:

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

$63\textup{ in}^2$ $\displaystyle 63\textup{ in}^2$

$52.5\textup{ in}^2$ $\displaystyle 52.5\textup{ in}^2$

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

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

Correct answer:

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

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:

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

Substitute in our side lengths.

$A=11\times 9$ $\displaystyle A=11\times 9$

A=99 $\displaystyle A=99$

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

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

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

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Example Question #4 : Geometry

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

Possible Answers:

$43\textup{ in}^2$ $\displaystyle 43\textup{ in}^2$

$40.5\textup{ in}^2$ $\displaystyle 40.5\textup{ in}^2$

$42\textup{ in}^2$ $\displaystyle 42\textup{ in}^2$

$30.5\textup{ in}^2$ $\displaystyle 30.5\textup{ in}^2$

$35\textup{ in}^2$ $\displaystyle 35\textup{ in}^2$

Correct answer:

$35\textup{ in}^2$ $\displaystyle 35\textup{ in}^2$

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:

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

Substitute in our side lengths.

$A=10\times 7$ $\displaystyle A=10\times 7$

A=70 $\displaystyle A=70$

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

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

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

Report an Error

Example Question #2 : Geometry

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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 $\displaystyle A=54$

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

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 $A=\frac{l\times w}{2}$ $\displaystyle A=\frac{l\times w}{2}$

Report an Error

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 $A=\frac{l\times w}{2}$ $\displaystyle A=\frac{l\times w}{2}$

Report an Error

Example Question #6 : Geometry

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

Possible Answers:

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

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

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

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

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

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 $A=\frac{l\times w}{2}$ $\displaystyle A=\frac{l\times w}{2}$

Report an Error

Example Question #7 : Geometry

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

Possible Answers:

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

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

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

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

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

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 $A=\frac{l\times w}{2}$ $\displaystyle A=\frac{l\times w}{2}$

Report an Error

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 $A=\frac{l\times w}{2}$ $\displaystyle A=\frac{l\times w}{2}$

Report an Error

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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 #1 : Geometry

Example Question #2 : Geometry

Example Question #1 : Geometry

Example Question #4 : Geometry

Example Question #2 : Geometry

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

Example Question #6 : Geometry

Example Question #7 : Geometry

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

All Common Core: 6th Grade Math Resources

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