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Basic Geometry : How to find the area of a rectangle

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Example Questions

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

If the perimeter of a rectangle is $\displaystyle 24$ , and the width of the rectangle is $\displaystyle 10$ , what is the area of the rectangle?

Possible Answers:

$\displaystyle 26$

$\displaystyle 22$

$\displaystyle 20$

$\displaystyle 24$

Correct answer:

$\displaystyle 20$

Explanation:

Recall how to find the perimeter of a rectangle:

$\text{Perimeter}=2(\text{length}+\text{width})$ $\displaystyle \text{Perimeter}=2(\text{length}+\text{width})$

Since we are given the width and the perimeter, we can solve for the length.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$ $\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{length}=\frac{\text{Perimeter}}{2}-\text{width}$ $\displaystyle \text{length}=\frac{\text{Perimeter}}{2}-\text{width}$

Substitute in the given values for the width and perimeter to find the length.

$\text{length}=\frac{24}{2}-10$ $\displaystyle \text{length}=\frac{24}{2}-10$

Simplify.

$\text{length}=12-10$ $\displaystyle \text{length}=12-10$

Solve.

$\text{length}=2$ $\displaystyle \text{length}=2$

Now, recall how to find the area of a rectangle.

$\text{Area}=\text{length}\times\text{width}$ $\displaystyle \text{Area}=\text{length}\times\text{width}$

Substitute in the values of the length and width to find the area.

$\text{Area}=10 \times 2$ $\displaystyle \text{Area}=10 \times 2$

Solve.

$\text{Area}=20$ $\displaystyle \text{Area}=20$

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Example Question #602 : Plane Geometry

If the perimeter of a rectangle is $\displaystyle 24$ , and the width of the rectangle is $\displaystyle 9$ , what is the area of the rectangle?

Possible Answers:

$\displaystyle 18$

$\displaystyle 36$

$\displaystyle 9$

$\displaystyle 27$

Correct answer:

$\displaystyle 27$

Explanation:

Recall how to find the perimeter of a rectangle:

$\text{Perimeter}=2(\text{length}+\text{width})$ $\displaystyle \text{Perimeter}=2(\text{length}+\text{width})$

Since we are given the width and the perimeter, we can solve for the length.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$ $\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{length}=\frac{\text{Perimeter}}{2}-\text{width}$ $\displaystyle \text{length}=\frac{\text{Perimeter}}{2}-\text{width}$

Substitute in the given values for the width and perimeter to find the length.

$\text{length}=\frac{24}{2}-9$ $\displaystyle \text{length}=\frac{24}{2}-9$

Simplify.

$\text{length}=12-9$ $\displaystyle \text{length}=12-9$

Solve.

$\text{length}=3$ $\displaystyle \text{length}=3$

Now, recall how to find the area of a rectangle.

$\text{Area}=\text{length}\times\text{width}$ $\displaystyle \text{Area}=\text{length}\times\text{width}$

Substitute in the values of the length and width to find the area.

$\text{Area}=3 \times 9$ $\displaystyle \text{Area}=3 \times 9$

Solve.

$\text{Area}=27$ $\displaystyle \text{Area}=27$

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

If the perimeter of a rectangle is $\displaystyle 24$ , and the width of the rectangle is $\displaystyle 8$ , what is the area of the rectangle?

Possible Answers:

$\displaystyle 32$

$\displaystyle 36$

$\displaystyle 44$

$\displaystyle 40$

Correct answer:

$\displaystyle 32$

Explanation:

Recall how to find the perimeter of a rectangle:

$\text{Perimeter}=2(\text{length}+\text{width})$ $\displaystyle \text{Perimeter}=2(\text{length}+\text{width})$

Since we are given the width and the perimeter, we can solve for the length.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$ $\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{length}=\frac{\text{Perimeter}}{2}-\text{width}$ $\displaystyle \text{length}=\frac{\text{Perimeter}}{2}-\text{width}$

Substitute in the given values for the width and perimeter to find the length.

$\text{length}=\frac{24}{2}-8$ $\displaystyle \text{length}=\frac{24}{2}-8$

Simplify.

$\text{length}=12-8$ $\displaystyle \text{length}=12-8$

Solve.

$\text{length}=4$ $\displaystyle \text{length}=4$

Now, recall how to find the area of a rectangle.

$\text{Area}=\text{length}\times\text{width}$ $\displaystyle \text{Area}=\text{length}\times\text{width}$

Substitute in the values of the length and width to find the area.

$\text{Area}=8 \times 4$ $\displaystyle \text{Area}=8 \times 4$

Solve.

$\text{Area}=32$ $\displaystyle \text{Area}=32$

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Example Question #601 : Basic Geometry

If the perimeter of a rectangle is $\displaystyle 24$ , and the width of the rectangle is $\displaystyle 7$ , what is the area of the rectangle?

Possible Answers:

$\displaystyle 40$

$\displaystyle 35$

$\displaystyle 30$

$\displaystyle 25$

Correct answer:

$\displaystyle 35$

Explanation:

Recall how to find the perimeter of a rectangle:

$\text{Perimeter}=2(\text{length}+\text{width})$ $\displaystyle \text{Perimeter}=2(\text{length}+\text{width})$

Since we are given the width and the perimeter, we can solve for the length.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$ $\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{length}=\frac{\text{Perimeter}}{2}-\text{width}$ $\displaystyle \text{length}=\frac{\text{Perimeter}}{2}-\text{width}$

Substitute in the given values for the width and perimeter to find the length.

$\text{length}=\frac{24}{2}-7$ $\displaystyle \text{length}=\frac{24}{2}-7$

Simplify.

$\text{length}=12-7$ $\displaystyle \text{length}=12-7$

Solve.

$\text{length}=5$ $\displaystyle \text{length}=5$

Now, recall how to find the area of a rectangle.

$\text{Area}=\text{length}\times\text{width}$ $\displaystyle \text{Area}=\text{length}\times\text{width}$

Substitute in the values of the length and width to find the area.

$\text{Area}=7 \times 5$ $\displaystyle \text{Area}=7 \times 5$

Solve.

$\text{Area}=35$ $\displaystyle \text{Area}=35$

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

A rectangle has a width of 5in $\displaystyle 5in$ , and a lenth of 12in $\displaystyle 12in$ . Find the perimeter.

Possible Answers:

39in $\displaystyle 39in$

60in $\displaystyle 60in$

30in $\displaystyle 30in$

25in $\displaystyle 25in$

34in $\displaystyle 34in$

Correct answer:

34in $\displaystyle 34in$

Explanation:

To find perimeter, you add the sides of the rectangle together. In this case, that would be:

$\displaystyle Perimeter = 12 + 12 + 5 + 5$

P = 34 $\displaystyle P = 34$

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

Find the area of a rectangle given length 7 and width 8.

Possible Answers:

$\displaystyle 15$

$\displaystyle 28$

$\displaystyle 56$

$\displaystyle 30$

Correct answer:

$\displaystyle 56$

Explanation:

To solve, simply use the formulaf or the area of a rectangle. Thus,

$\displaystyle A=l*w=7*8=56$

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Example Question #202 : Rectangles

Find the area of a rectangle given length of 5 and width of 7.

Possible Answers:

$\displaystyle 35$

$\displaystyle 24$

$\displaystyle 12$

$\frac{35}{2}$ $\displaystyle \frac{35}{2}$

Correct answer:

$\displaystyle 35$

Explanation:

To find the area of a rectangle multiply the width and base together.

To solve, simply use the formula for the area of a rectangle.

Let,

$\\w=7 \\l=5$ $\displaystyle \\w=7 \\l=5$ .

Thus,

$\displaystyle A=l*w=5*7=35$ .

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Example Question #52 : How To Find The Area Of A Rectangle

Find the area of a rectanlge with width 4 and length 7.

Possible Answers:

$\displaystyle 14$

$\displaystyle 11$

$\displaystyle 28$

$\displaystyle 22$

Correct answer:

$\displaystyle 28$

Explanation:

To solve, simply use the formula for the area of a rectangle.

$\displaystyle A=w*l=4*7=28$

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

Find the area of a square with side length 2.

Possible Answers:

$\displaystyle 4$

$\displaystyle 16$

$\displaystyle 2$

$\displaystyle 8$

Correct answer:

$\displaystyle 4$

Explanation:

To solve, simply use the formula for the area of a square. Thus,

$\displaystyle A=s^2=2^2=4$

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

If a rectangle has a width of $2.3\;cm$ $\displaystyle 2.3\;cm$ and a length that is double the width, what would be the area of the rectangle? Round to the nearest tenth.

Possible Answers:

$10.6\;cm^2$ $\displaystyle 10.6\;cm^2$

$6.9\;cm^2$ $\displaystyle 6.9\;cm^2$

$9.2\;cm^2$ $\displaystyle 9.2\;cm^2$

$5.3\;cm^2$ $\displaystyle 5.3\;cm^2$

$13.8\;cm^2$ $\displaystyle 13.8\;cm^2$

Correct answer:

$10.6\;cm^2$ $\displaystyle 10.6\;cm^2$

Explanation:

To calculate the area of a triangle, we want to multiply the length by the width. Since the length is twice that of the width, which is $2.3\;cm$ $\displaystyle 2.3\;cm$ , we can determine length as such:

$2.3\;cm\cdot2=4.6\;cm$ $\displaystyle 2.3\;cm\cdot2=4.6\;cm$

Now that we know the values for length and width, we can calculate the area of the triangle:

$Area=2.3\;cm\cdot4.6\;cm=10.6\;cm^2$ $\displaystyle Area=2.3\;cm\cdot4.6\;cm=10.6\;cm^2$

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Basic Geometry : How to find the area of a rectangle

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

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

Example Question #602 : Plane Geometry

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

Example Question #601 : Basic Geometry

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

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

Example Question #202 : Rectangles

Example Question #52 : How To Find The Area Of A Rectangle

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

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

All Basic Geometry Resources

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