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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 #23 : How To Find The Area Of A Rectangle

If the perimeter of a rectangle is , and the length of the rectangle is , what is the area of the rectangle?

Possible Answers:

155

145

135

125

Correct answer:

135

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:

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

From this equation, we can solve for the width.

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

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

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

$\text{Width}=\frac{48}{2}-15$

Simplify.

$\text{Width}=9$

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

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

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

$\text{Area}=15 \times 9$

Solve.

$\text{Area}=135$

Report an Error

Example Question #24 : How To Find The Area Of A Rectangle

If the perimeter of a rectangle is , and the length of the rectangle is , what is the area of the rectangle?

Possible Answers:

Correct answer:

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:

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

From this equation, we can solve for the width.

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

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

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

$\text{Width}=\frac{16}{2}-2$

Simplify.

$\text{Width}=6$

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

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

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

$\text{Area}=2 \times 6$

Solve.

$\text{Area}=12$

Report an Error

Example Question #25 : How To Find The Area Of A Rectangle

If the perimeter of a rectangle is , and the length of the rectangle is , what is the area of the rectangle?

Possible Answers:

Correct answer:

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:

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

From this equation, we can solve for the width.

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

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

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

$\text{Width}=\frac{20}{2}-5$

Simplify.

$\text{Width}=5$

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

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

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

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

Solve.

$\text{Area}=25$

Report an Error

Example Question #26 : How To Find The Area Of A Rectangle

If the perimeter of a rectangle is , and the length of the rectangle is , what is the area of the rectangle?

Possible Answers:

150

250

300

200

Correct answer:

200

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:

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

From this equation, we can solve for the width.

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

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

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

$\text{Width}=\frac{60}{2}-20$

Simplify.

$\text{Width}=10$

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

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

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

$\text{Area}=20 \times 10$

Solve.

$\text{Area}=200$

Report an Error

Example Question #585 : Plane Geometry

If the perimeter of a rectangle is , and the width of the rectangle is , what is the area of a rectangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the perimeter of a rectangle:

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

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

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

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

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

$\text{length}=\frac{36}{2}-17$

Simplify.

$\text{length}=18-17$

Solve.

$\text{length}=1$

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

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

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

$\text{Area}=17 \times 1$

Solve.

$\text{Area}=17$

Report an Error

Example Question #586 : Plane Geometry

If the perimeter of a rectangle is , and the width of the rectangle is , what is the area of the rectangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the perimeter of a rectangle:

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

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

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

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

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

$\text{length}=\frac{36}{2}-16$

Simplify.

$\text{length}=18-16$

Solve.

$\text{length}=2$

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

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

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

$\text{Area}=16 \times 2$

Solve.

$\text{Area}=32$

Report an Error

Example Question #31 : How To Find The Area Of A Rectangle

If the perimeter of a rectangle is , and the width of the rectangle is , what is the area of the rectangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the perimeter of a rectangle:

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

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

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

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

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

$\text{length}=\frac{36}{2}-15$

Simplify.

$\text{length}=18-15$

Solve.

$\text{length}=3$

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

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

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

$\text{Area}=15 \times 3$

Solve.

$\text{Area}=45$

Report an Error

Example Question #32 : How To Find The Area Of A Rectangle

If the perimeter of the rectangle is , and the width of the rectangle is , what is the area of the rectangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the perimeter of a rectangle:

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

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

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

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

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

$\text{length}=\frac{36}{2}-14$

Simplify.

$\text{length}=18-14$

Solve.

$\text{length}=4$

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

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

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

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

Solve.

$\text{Area}=56$

Report an Error

Example Question #589 : Plane Geometry

If the perimeter of a rectangle is , and the width of the rectangle is , what is the area of the rectangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the perimeter of a rectangle:

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

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

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

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

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

$\text{length}=\frac{36}{2}-13$

Simplify.

$\text{length}=18-13$

Solve.

$\text{length}=5$

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

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

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

$\text{Area}=13 \times 5$

Solve.

$\text{Area}=65$

Report an Error

Example Question #590 : Plane Geometry

If the perimeter of a rectangle is , and the width of the rectangle is , what is the area of the rectangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the perimeter of a rectangle:

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

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

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

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

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

$\text{length}=\frac{36}{2}-12=6$

Simplify.

$\text{length}=\frac{36}{2}-12=6$

Solve.

$\text{length}=\frac{36}{2}-12=6$

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

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

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

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

Solve.

$\text{Area}= 72$

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 #23 : How To Find The Area Of A Rectangle

Example Question #24 : How To Find The Area Of A Rectangle

Example Question #25 : How To Find The Area Of A Rectangle

Example Question #26 : How To Find The Area Of A Rectangle

Example Question #585 : Plane Geometry

Example Question #586 : Plane Geometry

Example Question #31 : How To Find The Area Of A Rectangle

Example Question #32 : How To Find The Area Of A Rectangle

Example Question #589 : Plane Geometry

Example Question #590 : Plane Geometry

All Basic Geometry Resources

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