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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

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

Report an Error

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

Report an Error

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

Report an Error

Example Question #461 : Plane Geometry

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

Possible Answers:

$26.5\textup{ in}^2$

$30\textup{ in}^2$

$27\textup{ in}^2$

$22\textup{ in}^2$

$32.5\textup{ in}^2$

Correct answer:

$27\textup{ in}^2$

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:

$A=l\times w$

Substitute in our side lengths.

$A=9\times 6$

A=54

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

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

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

Report an Error

Example Question #6 : 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:

$36\textup{ in}^2$

$20\textup{ in}^2$

$22\textup{ in}^2$

$40\textup{ in}^2$

$31.5\textup{ in}^2$

Correct answer:

$20\textup{ in}^2$

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:

$A=l\times w$

Substitute in our side lengths.

$A=8\times 5$

A=40

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

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

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

Report an Error

Example Question #7 : 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:

$14\textup{ in}^2$

$10.5\textup{ in}^2$

$12.5\textup{ in}^2$

$12\textup{ in}^2$

$13\textup{ in}^2$

Correct answer:

$14\textup{ in}^2$

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:

$A=l\times w$

Substitute in our side lengths.

$A=7\times 4$

A=28

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

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

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

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:

$75\textup{ in}^2$

$68\textup{ in}^2$

$72.5\textup{ in}^2$

$80\textup{ in}^2$

$70\textup{ in}^2$

Correct answer:

$70\textup{ in}^2$

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:

$A=l\times w$

Substitute in our side lengths.

$A=14\times 10$

A=140

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

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

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

Report an Error

Example Question #9 : 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:

$73.5\textup{ in}^2$

$86.5\textup{ in}^2$

$72\textup{ in}^2$

$80\textup{ in}^2$

$82.5\textup{ in}^2$

Correct answer:

$82.5\textup{ in}^2$

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:

$A=l\times w$

Substitute in our side lengths.

$A=15\times 11$

A=165

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

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

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

Report an Error

Example Question #10 : 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:

$98\textup{ in}^2$

$99.5\textup{ in}^2$

$90\textup{ in}^2$

$94.5\textup{ in}^2$

$96\textup{ in}^2$

Correct answer:

$96\textup{ in}^2$

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:

$A=l\times w$

Substitute in our side lengths.

$A=16\times 12$

A=192

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

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

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

Report an Error

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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 #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

Example Question #461 : Plane Geometry

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

Example Question #7 : Find Area Of Polygons: Ccss.Math.Content.6.G.A.1

Example Question #8 : Find Area Of Polygons: Ccss.Math.Content.6.G.A.1

Example Question #9 : Find Area Of Polygons: Ccss.Math.Content.6.G.A.1

Example Question #10 : Find Area Of Polygons: Ccss.Math.Content.6.G.A.1

All Common Core: 6th Grade Math Resources

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