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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

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All Basic Geometry Resources

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

Example Questions

Example Question #861 : Plane Geometry

Find the perimeter of a square that has side lengths of 8.9 .

Possible Answers:

32.6

27.6

38.6

35.6

Correct answer:

35.6

Explanation:

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

$\text{Perimeter}=4(\text{side length})$

For the given square,

$\text{Perimeter}=4(8.9)=35.6$

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Example Question #862 : Plane Geometry

Find the perimeter of a square that has side lengths of 102 .

Possible Answers:

308

608

408

1020

Correct answer:

408

Explanation:

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

$\text{Perimeter}=4(\text{side length})$

For the given square,

$\text{Perimeter}=4(102)=408$

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Example Question #863 : Plane Geometry

Find the perimeter of a square that has side lengths of 196.3 .

Possible Answers:

695.2

802.2

785.2

762.2

Correct answer:

785.2

Explanation:

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

$\text{Perimeter}=4(\text{side length})$

For the given square,

$\text{Perimeter}=4(196.3)=785.2$

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Example Question #864 : Plane Geometry

Find the perimeter of a square with the side lengths of $\frac{3}{4}$ .

Possible Answers:

Correct answer:

Explanation:

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

$\text{Perimeter}=4(\text{side length})$

For the given square,

$\text{Perimeter}=4\left(\frac{3}{4}\right)=3$

In this particular case the fours cancel out and our final answer is three.

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Example Question #865 : Plane Geometry

Find the perimeter of a square with side lengths of $\frac{5}{6}$ .

Possible Answers:

$\frac{1}{8}$

$\frac{20}{3}$

$\frac{5}{24}$

$\frac{10}{3}$

Correct answer:

$\frac{10}{3}$

Explanation:

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

$\text{Perimeter}=4(\text{side length})$

For the given square,

$\text{Perimeter}=4\left(\frac{5}{6}\right)=\frac{20}{6}=\frac{2\cdot 10}{2\cdot 3}=\frac{10}{3}$

Since there is a two in the numerator and a two in the denominator they cancel out which results in the simplified fraction.

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Example Question #456 : Quadrilaterals

If the diagonal of a square is $12\sqrt2$ , what is the perimeter of the square?

Possible Answers:

144

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 one side of the square.

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

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

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

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

For the square given in the question,

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

Simplify.

$\text{Side length}=12$

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

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

For the square in question,

$\text{Perimeter}=4\times 12$

Solve.

$\text{Perimeter}=48$

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Example Question #457 : Quadrilaterals

If the diagonal of a square is $2\sqrt2$ , what is the perimeter of the square?

Possible Answers:

$8\sqrt2$

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 one side of the square.

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

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

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

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

For the square given in the question,

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

Simplify.

$\text{Side length}=2$

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

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

For the square in question,

$\text{Perimeter}=4\times 2$

Solve.

$\text{Perimeter}=8$

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Example Question #21 : How To Find The Perimeter Of A Square

If the diagonal of a square is $7\sqrt2$ , what is the perimeter of the square?

Possible Answers:

$28\sqrt2$

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 one side of the square.

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

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

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

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

For the square given in the question,

$\text{Side length}=\frac{7\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=7$

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

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

For the square in question,

$\text{Perimeter}=4\times 7$

Solve.

$\text{Perimeter}=28$

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Example Question #461 : Quadrilaterals

If the diagonal of a square is $14\sqrt2$ , what is the perimeter of the square?

Possible Answers:

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 one side of the square.

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

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

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

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

For the square given in the question,

$\text{Side length}=\frac{14\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=14$

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

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

For the square in question,

$\text{Perimeter}=4\times 14$

Solve.

$\text{Perimeter}=56$

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Example Question #462 : Quadrilaterals

If the diagonal of a square is $10\sqrt2$ , what is the perimeter of the square?

Possible Answers:

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 one side of the square.

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

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

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

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

For the square given in the question,

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

Simplify.

$\text{Side length}=10$

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

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

For the square in question,

$\text{Perimeter}=4\times 10$

Solve.

$\text{Perimeter}=40$

Report an Error

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #861 : Plane Geometry

Example Question #862 : Plane Geometry

Example Question #863 : Plane Geometry

Example Question #864 : Plane Geometry

Example Question #865 : Plane Geometry

Example Question #456 : Quadrilaterals

Example Question #457 : Quadrilaterals

Example Question #21 : How To Find The Perimeter Of A Square

Example Question #461 : Quadrilaterals

Example Question #462 : Quadrilaterals

All Basic Geometry Resources

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