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Basic Geometry : Plane 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 #293 : Quadrilaterals

In square feet, find the area of a square that has side lengths of feet,

Possible Answers:

575

875

625

Correct answer:

625

Explanation:

Use the following formula to find the area of a square:

$\text{Area}=(\text{side length})^2$

For the given square,

$\text{Area}=25^2=625$

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Example Question #294 : Quadrilaterals

In square inches, find the area of a square that has side lengths of 100 inches.

Possible Answers:

100

1000

100000

10000

Correct answer:

10000

Explanation:

Use the following formula to find the area of a square:

$\text{Area}=(\text{side length})^2$

For the given square,

$\text{Area}=100^2=10000$

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Example Question #701 : Plane Geometry

In square inches, find the area of a square that has side lengths of $\sqrt2$ inches.

Possible Answers:

$\sqrt3$

$2\sqrt2$

Correct answer:

Explanation:

Use the following formula to find the area of a square:

$\text{Area}=(\text{side length})^2$

For the given square,

$\text{Area}=(\sqrt{2})^2=2$

Recall that when a square root is squared you are left with the number under the square root sign. This happens because when you square a number you are multiplying it by itself. In our case this is,

$(\sqrt{2})^2=\sqrt{2}\cdot \sqrt{2}$ .

From here we can use the property of multiplication and radicals to rewrite our expression as follows,

$\sqrt{2}\cdot \sqrt{2}=\sqrt{2\cdot 2}$

and when there are two numbers that are the same under a square root sign you bring out one and the other number and square root sign go away.

$\sqrt{2\cdot 2}=2$

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Example Question #43 : Squares

Find the area of a square that has side lengths of 0.2 .

Possible Answers:

0.02

0.04

0.4

Correct answer:

0.04

Explanation:

Use the following formula to find the area of a square:

$\text{Area}=(\text{side length})^2$

For the given square,

$\text{Area}=(0.2)^2=0.04$

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

$0.2\rightarrow 2$

Now we multiple the integers together.

$0.2\cdot 0.2\rightarrow 2\cdot 2=4$

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

Therefore our answer becomes,

$4\rightarrow 0.04$

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Example Question #18 : How To Find The Area Of A Square

In square units, find the area of a square that has side lengths of $\frac{1}{4}$ units.

Possible Answers:

$\frac{1}{16}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{16}$

Explanation:

Use the following formula to find the area of a square:

$\text{Area}=(\text{side length})^2$

For the given square,

$\text{Area}=\left(\frac{1}{4}\right)^2=\frac{1}{16}$

When squarring a fraction we need to square both the numerator and the denominator.

$\left( \frac{1}{4}\right)^2=\frac{1^2}{4^2}=\frac{1\cdot 1}{4\cdot 4}=\frac{1}{16}$

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Example Question #702 : Plane Geometry

In square units, find the area of the square with side lengths $\frac{2}{3}$ units.

Possible Answers:

$\frac{4}{3}$

$\frac{5}{6}$

$\frac{1}{3}$

$\frac{4}{9}$

Correct answer:

$\frac{4}{9}$

Explanation:

Use the following formula to find the area of a square:

$\text{Area}=(\text{side length})^2$

For the given square,

$\text{Area}=\left(\frac{2}{3}\right)^2=\frac{4}{9}$

When squarring a fraction we need to square both the numerator and the denominator.

$\left(\frac{2}{3}\right)^2==\frac{2^2}{3^2}=\frac{2\cdot 2}{3\cdot 3}=\frac{4}{9}$

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Example Question #297 : Quadrilaterals

In square units, find the area of the square with side length 0.6 units.

Possible Answers:

1.2

0.12

0.24

0.36

Correct answer:

0.36

Explanation:

Use the following formula to find the area of a square:

$\text{Area}=(\text{side length})^2$

For the given square,

$\text{Area}=0.6^2=0.36$

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

$0.6\rightarrow 6$

Now we multiple the integers together.

$0.6\cdot 0.6\rightarrow 6\cdot 6=36$

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

Therefore our answer becomes,

$36\rightarrow 0.36$

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Example Question #703 : Plane Geometry

In square units, find the area of a square with side lengths 0.7 units.

Possible Answers:

0.21

0.49

1.4

0.14

Correct answer:

0.49

Explanation:

Use the following formula to find the area of a square:

$\text{Area}=(\text{side length})^2$

For the given square,

$\text{Area}=0.7^2=0.49$

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

$0.7\rightarrow 7$

Now we multiple the integers together.

$0.7\cdot 0.7\rightarrow 7\cdot 7=49$

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

Therefore our answer becomes,

$49\rightarrow 0.49$

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Example Question #301 : Quadrilaterals

In square units, find the area of the square with side lengths of 0.8 .

Possible Answers:

1.6

0.16

0.72

0.64

Correct answer:

0.64

Explanation:

Use the following formula to find the area of a square:

$\text{Area}=(\text{side length})^2$

For the given square,

$\text{Area}=0.8^2=0.64$

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

$0.8\rightarrow 8$

Now we multiple the integers together.

$0.8\cdot 0.8\rightarrow 8\cdot 8=64$

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

Therefore our answer becomes,

$64\rightarrow 0.64$

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Example Question #302 : Quadrilaterals

If the perimeter of a square is 160 , find the area of the square.

Possible Answers:

3200

6400

2400

1600

Correct answer:

1600

Explanation:

First, recall how to find the perimeter of a square.

$\text{Perimeter}=4\times\text{side length}$

From this equation, we can solve for the side length of a square.

$\text{Side length}=\frac{\text{Perimeter}}{4}$

For the given square,

$\text{Side length}=\frac{160}{4}=40$

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

$\text{Area}=\text{side length}^2$

For the square in question, we can plug in the side length we found from the perimeter to find the area.

$\text{Area}=40^2=1600$

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #293 : Quadrilaterals

Example Question #294 : Quadrilaterals

Example Question #701 : Plane Geometry

Example Question #43 : Squares

Example Question #18 : How To Find The Area Of A Square

Example Question #702 : Plane Geometry

Example Question #297 : Quadrilaterals

Example Question #703 : Plane Geometry

Example Question #301 : Quadrilaterals

Example Question #302 : Quadrilaterals

All Basic Geometry Resources

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