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Common Core: 6th Grade Math : Geometry

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 #47 : How To Find The Area Of A Triangle

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

Possible Answers:

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

$64.5\textup{ in}^2$ $\displaystyle 64.5\textup{ in}^2$

$60.5\textup{ in}^2$ $\displaystyle 60.5\textup{ in}^2$

$62\textup{ in}^2$ $\displaystyle 62\textup{ in}^2$

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

Correct answer:

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

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.

$A=14\times 9$ $\displaystyle A=14\times 9$

A=126 $\displaystyle A=126$

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 $\displaystyle 2$.

$126\div 2= 63\textup{ in}^2$ $\displaystyle 126\div 2= 63\textup{ in}^2$

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 #42 : How To Find The Area Of A Triangle

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

Possible Answers:

$50.5\textup{ in}^2$ $\displaystyle 50.5\textup{ in}^2$

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

$56\textup{ in}^2$ $\displaystyle 56\textup{ in}^2$

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

$54\textup{ in}^2$ $\displaystyle 54\textup{ in}^2$

Correct answer:

$56\textup{ in}^2$ $\displaystyle 56\textup{ in}^2$

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.

$A=14\times 8$ $\displaystyle A=14\times 8$

A=112 $\displaystyle A=112$

$112\div 2= 56\textup{ in}^2$ $\displaystyle 112\div 2= 56\textup{ in}^2$

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 #49 : How To Find The Area Of A Triangle

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

Possible Answers:

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

$48.5\textup{ in}^2$ $\displaystyle 48.5\textup{ in}^2$

$50\textup{ in}^2$ $\displaystyle 50\textup{ in}^2$

$49\textup{ in}^2$ $\displaystyle 49\textup{ in}^2$

$43.5\textup{ in}^2$ $\displaystyle 43.5\textup{ in}^2$

Correct answer:

$49\textup{ in}^2$ $\displaystyle 49\textup{ in}^2$

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.

$A=14\times 7$ $\displaystyle A=14\times 7$

A=98 $\displaystyle A=98$

$98\div 2= 49\textup{ in}^2$ $\displaystyle 98\div 2= 49\textup{ in}^2$

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 #50 : How To Find The Area Of A Triangle

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

Possible Answers:

$42.5\textup{ in}^2$ $\displaystyle 42.5\textup{ in}^2$

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

$38\textup{ in}^2$ $\displaystyle 38\textup{ in}^2$

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

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

Correct answer:

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

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.

$A=14\times 6$ $\displaystyle A=14\times 6$

A=84 $\displaystyle A=84$

$84\div 2= 42\textup{ in}^2$ $\displaystyle 84\div 2= 42\textup{ in}^2$

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:

$79.5\textup{ in}^2$ $\displaystyle 79.5\textup{ in}^2$

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

$78\textup{ in}^2$ $\displaystyle 78\textup{ in}^2$

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

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

Correct answer:

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

Explanation:

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

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.

$A=15\times 10$ $\displaystyle A=15\times 10$

A=150 $\displaystyle A=150$

$150\div 2= 75\textup{ in}^2$ $\displaystyle 150\div 2= 75\textup{ in}^2$

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 #51 : How To Find The Area Of A Triangle

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

Possible Answers:

$70.5\textup{ in}^2$ $\displaystyle 70.5\textup{ in}^2$

$65\textup{ in}^2$ $\displaystyle 65\textup{ in}^2$

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

$67.5\textup{ in}^2$ $\displaystyle 67.5\textup{ in}^2$

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

Correct answer:

$67.5\textup{ in}^2$ $\displaystyle 67.5\textup{ in}^2$

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.

$A=15\times 9$ $\displaystyle A=15\times 9$

A=135 $\displaystyle A=135$

$135\div 2= 67.5\textup{ in}^2$ $\displaystyle 135\div 2= 67.5\textup{ in}^2$

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 #53 : How To Find The Area Of A Triangle

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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.

$A=15\times 8$ $\displaystyle A=15\times 8$

A=120 $\displaystyle A=120$

$120\div 2= 60\textup{ in}^2$ $\displaystyle 120\div 2= 60\textup{ in}^2$

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 #54 : How To Find The Area Of A Triangle

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

Possible Answers:

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

$54.5\textup{ in}^2$ $\displaystyle 54.5\textup{ in}^2$

$56\textup{ in}^2$ $\displaystyle 56\textup{ in}^2$

$53\textup{ in}^2$ $\displaystyle 53\textup{ in}^2$

$50.5\textup{ in}^2$ $\displaystyle 50.5\textup{ in}^2$

Correct answer:

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

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.

$A=15\times 7$ $\displaystyle A=15\times 7$

A=105 $\displaystyle A=105$

$105\div 2= 52.5\textup{ in}^2$ $\displaystyle 105\div 2= 52.5\textup{ in}^2$

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 #55 : How To Find The Area Of A Triangle

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

Possible Answers:

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

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

$84\textup{ in}^2$ $\displaystyle 84\textup{ in}^2$

$86\textup{ in}^2$ $\displaystyle 86\textup{ in}^2$

$89.5\textup{ in}^2$ $\displaystyle 89.5\textup{ in}^2$

Correct answer:

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

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.

$A=16\times 11$ $\displaystyle A=16\times 11$

A=176 $\displaystyle A=176$

$176\div 2= 88\textup{ in}^2$ $\displaystyle 176\div 2= 88\textup{ in}^2$

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 #56 : How To Find The Area Of A Triangle

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

Possible Answers:

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

$78\textup{ in}^2$ $\displaystyle 78\textup{ in}^2$

$83\textup{ in}^2$ $\displaystyle 83\textup{ in}^2$

$77.5\textup{ in}^2$ $\displaystyle 77.5\textup{ in}^2$

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

Correct answer:

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

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.

$A=16\times 10$ $\displaystyle A=16\times 10$

A=160 $\displaystyle A=160$

$160\div 2= 80\textup{ in}^2$ $\displaystyle 160\div 2= 80\textup{ in}^2$

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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All Common Core: 6th Grade Math Resources

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Common Core: 6th Grade Math : Geometry

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

All Common Core: 6th Grade Math Resources

Example Questions

Example Question #47 : How To Find The Area Of A Triangle

Example Question #42 : How To Find The Area Of A Triangle

Example Question #49 : How To Find The Area Of A Triangle

Example Question #50 : How To Find The Area Of A Triangle

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

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

Example Question #53 : How To Find The Area Of A Triangle

Example Question #54 : How To Find The Area Of A Triangle

Example Question #55 : How To Find The Area Of A Triangle

Example Question #56 : How To Find The Area Of A Triangle

All Common Core: 6th Grade Math Resources

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