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Basic Geometry : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

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9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #14 : How To Find The Area Of A Rectangle

What is the area of a rectangle that has a length of $\displaystyle 85$ and a width of 0.75 $\displaystyle 0.75$?

Possible Answers:

76.75 $\displaystyle 76.75$

63.75 $\displaystyle 63.75$

55.25 $\displaystyle 55.25$

69.75 $\displaystyle 69.75$

Correct answer:

63.75 $\displaystyle 63.75$

Explanation:

Recall how to find the area of a rectangle:

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

Now, plug in the given length and width to find the area.

When multiplying decimals together first move the decimal over so that the number is a whole integer.

$0.75\rightarrow 75$ $\displaystyle 0.75\rightarrow 75$

Now we multiple the integers together.

$0.75\cdot 85\rightarrow 75\cdot 85=6375$ $\displaystyle 0.75\cdot 85\rightarrow 75\cdot 85=6375$

From here, we need to move the decimal place back. In this particular problem we moved the decimal over a total of two decimal places.

Therefore our answer becomes,

$6375\rightarrow 63.75$ $\displaystyle 6375\rightarrow 63.75$

$\text{Area}=85 \times 0.75= 63.75$ $\displaystyle \text{Area}=85 \times 0.75= 63.75$

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Example Question #15 : How To Find The Area Of A Rectangle

What is the area of a rectangle that has a length of $\displaystyle 63$ and a width of $\frac{1}{7}$ $\displaystyle \frac{1}{7}$?

Possible Answers:

$\displaystyle 7$

$\displaystyle 10$

$\displaystyle 8$

$\displaystyle 9$

Correct answer:

$\displaystyle 9$

Explanation:

Recall how to find the area of a rectangle:

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

Now, plug in the given length and width to find the area.

When multiplying fractions, multiply the numerators together and multiply the denominators together. After multiplication is done, find common factors in the numerator and denominator to cancel out and completely simplify the fraction. In this particular case the integer can be written as a fraction by putting it over one.

$\textup{Area}=\frac{63}{1}\times \frac{1}{7}$ $\displaystyle \textup{Area}=\frac{63}{1}\times \frac{1}{7}$

$\text{Area}= \frac{1 \times 63 }{7\times 1}= \frac{63}{7}=\frac{7\cdot 9}{7}=9$ $\displaystyle \text{Area}= \frac{1 \times 63 }{7\times 1}= \frac{63}{7}=\frac{7\cdot 9}{7}=9$

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Example Question #16 : How To Find The Area Of A Rectangle

If the perimeter of a rectangle is $\displaystyle 24$, and the length of the rectangle is $\displaystyle 5$, what is the area of the rectangle?

Possible Answers:

$\displaystyle 40$

$\displaystyle 25$

$\displaystyle 30$

$\displaystyle 35$

Correct answer:

$\displaystyle 35$

Explanation:

First, use the information given about the perimeter to find the width of the rectangle.

Recall how to find the perimeter of a rectangle:

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

From this equation, we can solve for the width.

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

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

Substitute in the information from the question to find the width of the rectangle.

$\text{Width}=\frac{24}{2}-5=7$ $\displaystyle \text{Width}=\frac{24}{2}-5=7$

Simplify.

$\text{Width}=7$ $\displaystyle \text{Width}=7$

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 information about the length and width to find the area for the rectangle in question.

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

Solve.

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

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Example Question #17 : How To Find The Area Of A Rectangle

If the perimeter of a rectangle is $\displaystyle 18$, and the length of the rectangle is $\displaystyle 6$, what is the area of the rectangle?

Possible Answers:

$\displaystyle 21$

$\displaystyle 12$

$\displaystyle 15$

$\displaystyle 18$

Correct answer:

$\displaystyle 18$

Explanation:

First, use the information given about the perimeter to find the width of the rectangle.

Recall how to find the perimeter of a rectangle:

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

From this equation, we can solve for the width.

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

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

Substitute in the information from the question to find the width of the rectangle.

$\text{Width}=\frac{18}{2}-6$ $\displaystyle \text{Width}=\frac{18}{2}-6$

Simplify.

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

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 information about the length and width to find the area for the rectangle in question.

$\text{Area}=6 \times 3$ $\displaystyle \text{Area}=6 \times 3$

Solve.

$\text{Area}=18$ $\displaystyle \text{Area}=18$

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Example Question #165 : Rectangles

If the perimeter of a rectangle is $\displaystyle 36$, and the length of the rectangle is $\displaystyle 12$, what is the area of the rectangle?

Possible Answers:

$\displaystyle 72$

$\displaystyle 66$

$\displaystyle 78$

$\displaystyle 85$

Correct answer:

$\displaystyle 72$

Explanation:

First, use the information given about the perimeter to find the width of the rectangle.

Recall how to find the perimeter of a rectangle:

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

From this equation, we can solve for the width.

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

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

Substitute in the information from the question to find the width of the rectangle.

$\text{Width}=\frac{36}{2}-12$ $\displaystyle \text{Width}=\frac{36}{2}-12$

Simplify.

$\text{Width}=6$ $\displaystyle \text{Width}=6$

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 information about the length and width to find the area for the rectangle in question.

$\text{Area}=12 \times 6$ $\displaystyle \text{Area}=12 \times 6$

Solve.

$\text{Area}=72$ $\displaystyle \text{Area}=72$

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Example Question #21 : How To Find The Area Of A Rectangle

If the perimeter of a rectangle is $\displaystyle 50$, and the length of the rectangle is $\displaystyle 13$, what is the area of the rectangle?

Possible Answers:

168 $\displaystyle 168$

156 $\displaystyle 156$

132 $\displaystyle 132$

144 $\displaystyle 144$

Correct answer:

156 $\displaystyle 156$

Explanation:

First, use the information given about the perimeter to find the width of the rectangle.

Recall how to find the perimeter of a rectangle:

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

From this equation, we can solve for the width.

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

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

Substitute in the information from the question to find the width of the rectangle.

$\text{Width}=\frac{50}{2}-13$ $\displaystyle \text{Width}=\frac{50}{2}-13$

Simplify.

$\text{Width}=12$ $\displaystyle \text{Width}=12$

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 information about the length and width to find the area for the rectangle in question.

$\text{Area}=13 \times 12$ $\displaystyle \text{Area}=13 \times 12$

Solve.

$\text{Area}=156$ $\displaystyle \text{Area}=156$

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Example Question #22 : How To Find The Area Of A Rectangle

If the perimeter of a rectangle is $\displaystyle 28$, and the length of the rectangle is $\displaystyle 13$, what is the area of the rectangle?

Possible Answers:

$\displaystyle 13$

$\displaystyle 18$

$\displaystyle 26$

$\displaystyle 14$

Correct answer:

$\displaystyle 13$

Explanation:

First, use the information given about the perimeter to find the width of the rectangle.

Recall how to find the perimeter of a rectangle:

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

From this equation, we can solve for the width.

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

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

Substitute in the information from the question to find the width of the rectangle.

$\text{Width}=\frac{28}{2}-13$ $\displaystyle \text{Width}=\frac{28}{2}-13$

Simplify.

$\text{Width}=1$ $\displaystyle \text{Width}=1$

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 information about the length and width to find the area for the rectangle in question.

$\text{Area}=13 \times 1$ $\displaystyle \text{Area}=13 \times 1$

Solve.

$\text{Area}=13$ $\displaystyle \text{Area}=13$

Report an Error

Example Question #163 : Rectangles

If the perimeter of a rectangle is $\displaystyle 48$, and the length of the rectangle is $\displaystyle 10$, what is the area of the rectangle?

Possible Answers:

280 $\displaystyle 280$

160 $\displaystyle 160$

140 $\displaystyle 140$

130 $\displaystyle 130$

Correct answer:

140 $\displaystyle 140$

Explanation:

First, use the information given about the perimeter to find the width of the rectangle.

Recall how to find the perimeter of a rectangle:

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

From this equation, we can solve for the width.

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

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

Substitute in the information from the question to find the width of the rectangle.

$\text{Width}=\frac{48}{2}-10$ $\displaystyle \text{Width}=\frac{48}{2}-10$

Simplify.

$\text{Width}=14$ $\displaystyle \text{Width}=14$

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 information about the length and width to find the area for the rectangle in question.

$\text{Area}=10 \times 14$ $\displaystyle \text{Area}=10 \times 14$

Solve.

$\text{Area}=140$ $\displaystyle \text{Area}=140$

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Example Question #571 : Basic Geometry

If the perimeter of a rectangle is $\displaystyle 70$, and the length of the rectangle is $\displaystyle 25$, what is the area of the rectangle?

Possible Answers:

350 $\displaystyle 350$

250 $\displaystyle 250$

175 $\displaystyle 175$

300 $\displaystyle 300$

Correct answer:

250 $\displaystyle 250$

Explanation:

First, use the information given about the perimeter to find the width of the rectangle.

Recall how to find the perimeter of a rectangle:

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

From this equation, we can solve for the width.

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

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

Substitute in the information from the question to find the width of the rectangle.

$\text{Width}=\frac{70}{2}-25$ $\displaystyle \text{Width}=\frac{70}{2}-25$

Simplify.

$\text{Width}=10$ $\displaystyle \text{Width}=10$

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 information about the length and width to find the area for the rectangle in question.

$\text{Area}=25 \times 10$ $\displaystyle \text{Area}=25 \times 10$

Solve.

$\text{Area}=250$ $\displaystyle \text{Area}=250$

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Example Question #171 : Rectangles

If the perimeter of a rectangle is $\displaystyle 40$, and the length fo the rectangle is $\displaystyle 5$, what is the area of the rectangle?

Possible Answers:

$\displaystyle 65$

$\displaystyle 95$

$\displaystyle 85$

$\displaystyle 75$

Correct answer:

$\displaystyle 75$

Explanation:

First, use the information given about the perimeter to find the width of the rectangle.

Recall how to find the perimeter of a rectangle:

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

From this equation, we can solve for the width.

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

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

Substitute in the information from the question to find the width of the rectangle.

$\text{Width}=\frac{40}{2}-5$ $\displaystyle \text{Width}=\frac{40}{2}-5$

Simplify.

$\text{Width}=15$ $\displaystyle \text{Width}=15$

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 information about the length and width to find the area for the rectangle in question.

$\text{Area}=5 \times 15$ $\displaystyle \text{Area}=5 \times 15$

Solve.

$\text{Area}=75$ $\displaystyle \text{Area}=75$

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Basic Geometry : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #14 : How To Find The Area Of A Rectangle

Example Question #15 : How To Find The Area Of A Rectangle

Example Question #16 : How To Find The Area Of A Rectangle

Example Question #17 : How To Find The Area Of A Rectangle

Example Question #165 : Rectangles

Example Question #21 : How To Find The Area Of A Rectangle

Example Question #22 : How To Find The Area Of A Rectangle

Example Question #163 : Rectangles

Example Question #571 : Basic Geometry

Example Question #171 : Rectangles

All Basic Geometry Resources

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