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Basic Geometry : Quadrilaterals

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #599 : 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.

$\text{length}=\frac{20}{2}-9$

Simplify.

$\text{length}=10-9$

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.

$\text{Area}=9 \times 1$

Solve.

$\text{Area}=9$

Report an Error

Example Question #600 : 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.

$\text{length}=\frac{12}{2}-1$

Simplify.

$\text{length}=6-1$

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.

$\text{Area}=5 \times 1$

Solve.

$\text{Area}=5$

Report an Error

Example Question #191 : Quadrilaterals

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.

$\text{length}=\frac{14}{2}-6$

Simplify.

$\text{length}=7-6$

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.

$\text{Area}=6 \times 1$

Solve.

$\text{Area}= 6$

Report an Error

Example Question #602 : 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.

$\text{length}=\frac{30}{2}-14$

Simplify.

$\text{length}=15-14$

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.

$\text{Area}=14 \times 1$

Solve.

$\text{Area}=14$

Report an Error

Example Question #603 : 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.

$\text{length}=\frac{22}{2}-10$

Simplify.

$\text{length}=11-10$

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.

$\text{Area}=10 \times 1$

Solve.

$\text{Area}=10$

Report an Error

Example Question #604 : 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.

$\text{length}=\frac{24}{2}-11$

Simplify.

$\text{length}=12-11$

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.

$\text{Area}=11 \times 1$

Solve.

$\text{Area}=11$

Report an Error

Example Question #51 : 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.

$\text{length}=\frac{24}{2}-10$

Simplify.

$\text{length}=12-10$

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.

$\text{Area}=10 \times 2$

Solve.

$\text{Area}=20$

Report an Error

Example Question #602 : 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.

$\text{length}=\frac{24}{2}-9$

Simplify.

$\text{length}=12-9$

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.

$\text{Area}=3 \times 9$

Solve.

$\text{Area}=27$

Report an Error

Example Question #53 : 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.

$\text{length}=\frac{24}{2}-8$

Simplify.

$\text{length}=12-8$

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.

$\text{Area}=8 \times 4$

Solve.

$\text{Area}=32$

Report an Error

Example Question #54 : 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.

$\text{length}=\frac{24}{2}-7$

Simplify.

$\text{length}=12-7$

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.

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

Solve.

$\text{Area}=35$

Report an Error

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Basic Geometry : Quadrilaterals

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #599 : Plane Geometry

Example Question #600 : Plane Geometry

Example Question #191 : Quadrilaterals

Example Question #602 : Plane Geometry

Example Question #603 : Plane Geometry

Example Question #604 : Plane Geometry

Example Question #51 : How To Find The Area Of A Rectangle

Example Question #602 : Plane Geometry

Example Question #53 : How To Find The Area Of A Rectangle

Example Question #54 : How To Find The Area Of A Rectangle

All Basic Geometry Resources

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