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Basic Geometry : Quadrilaterals

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Example Questions

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

Example Question #181 : 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.

$\text{length}=\frac{36}{2}-11$

Simplify.

$\text{length}=18-11$

Solve.

$\text{length}=7$

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.

$\text{Area}=11 \times 7$

Solve.

$\text{Area}=77$

Report an Error

Example Question #592 : 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:

100

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.

$\text{length}=\frac{36}{2}-10$

Simplify.

$\text{length}=18-10$

Solve.

$\text{length}=8$

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.

$\text{Area}=10 \times 8$

Solve.

$\text{Area}=80$

Report an Error

Example Question #591 : Basic Geometry

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

Possible Answers:

13.5

23.5

Correct answer:

13.5

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.

$\text{length}=\frac{15}{2}-3$

Simplify.

$\text{length}=7.5-3$

Solve.

$\text{length}=4.5$

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.

$\text{Area}=3 \times 4.5$

Solve.

$\text{Area}=13.5$

Report an Error

Example Question #592 : Basic Geometry

If the perimeter of a rectangle is 100 , and the width of the rectangle is , what is the area of the rectangle?

Possible Answers:

546

456

471

330

Correct answer:

456

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.

$\text{length}=\frac{100}{2}-12$

Simplify.

$\text{length}=50-12$

Solve.

$\text{length}=38$

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.

$\text{Area}=12 \times 38$

Solve.

$\text{Area}=456$

Report an Error

Example Question #595 : 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:

216

188

112

Correct answer:

216

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.

$\text{length}=\frac{60}{2}-12$

Simplify.

$\text{length}=30-12$

Solve.

$\text{length}=18$

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.

$\text{Area}=12 \times 18$

Solve.

$\text{Area}=216$

Report an Error

Example Question #596 : 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:

108

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.

$\text{length}=\frac{36}{2}-9$

Simplify.

$\text{length}=18-9$

Solve.

$\text{length}=9$

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.

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

Solve.

$\text{Area}=81$

Report an Error

Example Question #591 : 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.

$\text{length}=\frac{16}{2}-7$

Simplify.

$\text{length}=8-7$

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.

$\text{Area}=7 \times 1$

Solve.

$\text{Area}=7$

Report an Error

Example Question #598 : 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.

$\text{length}=\frac{10}{2}-1$

Simplify.

$\text{length}=5-1$

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.

$\text{Area}=4 \times 1$

Solve.

$\text{Area}= 4$

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 #589 : Plane Geometry

Example Question #590 : Plane Geometry

Example Question #181 : Quadrilaterals

Example Question #592 : Plane Geometry

Example Question #591 : Basic Geometry

Example Question #592 : Basic Geometry

Example Question #595 : Plane Geometry

Example Question #596 : Plane Geometry

Example Question #591 : Plane Geometry

Example Question #598 : Plane Geometry

All Basic Geometry Resources

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