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Basic Geometry : Quadrilaterals

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

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Example Question #312 : Squares

If the diagonal of a square is $88\sqrt2$ , what is the length of one side of the square?

Possible Answers:

$44\sqrt2$

$88\sqrt2$

176

Correct answer:

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

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

$\text{Diagonal}=(\text{side length})\sqrt2$

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{88\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=88$

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Example Question #964 : Plane Geometry

If the diagonal of a square is $97\sqrt2$ , what is the length of one side of the square?

Possible Answers:

157

196

Correct answer:

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

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

$\text{Diagonal}=(\text{side length})\sqrt2$

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{97\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=97$

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Example Question #42 : How To Find The Length Of The Side Of A Square

If the diagonal of a square is , what is the length of one side of the square?

Possible Answers:

$6\sqrt2$

$12\sqrt2$

Correct answer:

$6\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

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

$\text{Diagonal}=(\text{side length})\sqrt2$

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{12}{\sqrt{2}}$

Multiply the top and bottom of the fraction by one in the form of $\frac{\sqrt{2}}{\sqrt{2}}$

$\text{Side length}=\frac{12}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}$

Solve.

$\text{Side length}=\frac{12\sqrt2}{2}$

Simplify.

$\text{Side length}=6\sqrt2$

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Example Question #311 : Squares

If the diagonal of a square is , what is the length of one side of the square?

Possible Answers:

$10\sqrt2$

$5\sqrt2$

Correct answer:

$5\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

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

$\text{Diagonal}=(\text{side length})\sqrt2$

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{10}{\sqrt{2}}=\frac{10\sqrt2}{2}=5\sqrt2$

Multiply the top and bottom of the fraction by one in the form of $\frac{\sqrt{2}}{\sqrt{2}}$

$\text{Side length}=\frac{10}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}$

Silve.

$\text{Side length}=\frac{10\sqrt2}{2}$

Simplify.

$\text{Side length}=5\sqrt2$

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Example Question #316 : Squares

Given that the area of a square is 16 cm^2 , solve for the lengths of the sides.

Possible Answers:

8cm

7cm

4cm

9cm

3cm

Correct answer:

4cm

Explanation:

To find the answer to this question, the formula for area is needed.

Area = Side(Side)

Plugging in the numbers, we get:

16 = Side (Side)

This is also written as

16 = Side^2

Take the sqare root of 16, and you get:

4cm = side

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Example Question #51 : How To Find The Length Of The Side Of A Square

Find the side length of a square given the area is 144.

Possible Answers:

Correct answer:

Explanation:

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

$A=s^2\Rightarrow s=\sqrt{A}$

$s=\sqrt{144}=12$

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Example Question #52 : How To Find The Length Of The Side Of A Square

Oscar recently built his first home, with a floor plan that is both a perfect square and has an area of $729\;ft^2$ . What is the length for the sides of Oscar's new home?

Possible Answers:

$27\;ft$

$21\;ft$

$24\;ft$

$30\;ft$

$33\;ft$

Correct answer:

$27\;ft$

Explanation:

Since both sides of a square are of equal length, we can use this formula to determine the length of both sides.

$\\Area=length\cdot length\\ 729\;ft^2=length^2\\length=\sqrt{729\;ft^2}\\length=27\;ft$

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Example Question #51 : How To Find The Length Of The Side Of A Square

A cube has a volume of 512in^3 . What is the length of one of the sides of one of its faces?

Possible Answers:

15in

8in

4in

10in

12in

Correct answer:

8in

Explanation:

The volume of a cube is found by multiplying the width, height, and depth. Since all sides are equal, the formula would look like V=s^3 . Since we know the volume, we can take the cube root of that volume to get the individual side length.

512=s^3

What number cubed equals 512? 8 cubed gives 512.

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Example Question #54 : How To Find The Length Of The Side Of A Square

The diagonal of a square is $\sqrt{8}$ centimeters. What is the length of each side?

Possible Answers:

2 cm

6cm

8cm

4 cm

Correct answer:

2 cm

Explanation:

To solve, set up an equation using the Pythagorean Theorem:

$x^2 + x^2 = \sqrt{8}^2$

x^2 + x^2 = 8

2x^2 = 8 divide both sides by 2

x^2 = 4 take the square root of both sides

x = 2

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Example Question #55 : How To Find The Length Of The Side Of A Square

The perimeter of a square is 56cm. What is the length of the sides?

Possible Answers:

14cm

56cm

224cm

10cm

28cm

Correct answer:

14cm

Explanation:

The perimeter of a square is the sum of all the sides, or 4 times the length of one side.

4*side=Perimeter

$side=\frac{Perimeter}{4}$

$side = \frac{56}{4}$

side=14cm

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Basic Geometry : Quadrilaterals

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #312 : Squares

Example Question #964 : Plane Geometry

Example Question #42 : How To Find The Length Of The Side Of A Square

Example Question #311 : Squares

Example Question #316 : Squares

Example Question #51 : How To Find The Length Of The Side Of A Square

Example Question #52 : How To Find The Length Of The Side Of A Square

Example Question #51 : How To Find The Length Of The Side Of A Square

Example Question #54 : How To Find The Length Of The Side Of A Square

Example Question #55 : How To Find The Length Of The Side Of A Square

All Basic Geometry Resources

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