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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 #591 : Plane Geometry

If the perimeter of a rectangle is $\displaystyle 36$, and the width of the rectangle is $\displaystyle 11$, what is the area of the rectangle?

Possible Answers:

$\displaystyle 91$

$\displaystyle 84$

$\displaystyle 98$

$\displaystyle 77$

Correct answer:

$\displaystyle 77$

Explanation:

Recall how to find the perimeter of a rectangle:

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

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

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

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

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

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

Simplify.

$\text{length}=18-11$ $\displaystyle \text{length}=18-11$

Solve.

$\text{length}=7$ $\displaystyle \text{length}=7$

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

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

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

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

Solve.

$\text{Area}=77$ $\displaystyle \text{Area}=77$

Report an Error

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

If the perimeter of a rectangle is $\displaystyle 36$, and the width of the rectangle is $\displaystyle 10$, what is the area of the rectangle?

Possible Answers:

$\displaystyle 70$

$\displaystyle 80$

$\displaystyle 90$

100 $\displaystyle 100$

Correct answer:

$\displaystyle 80$

Explanation:

Recall how to find the perimeter of a rectangle:

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

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

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

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

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

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

Simplify.

$\text{length}=18-10$ $\displaystyle \text{length}=18-10$

Solve.

$\text{length}=8$ $\displaystyle \text{length}=8$

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

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

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

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

Solve.

$\text{Area}=80$ $\displaystyle \text{Area}=80$

Report an Error

Example Question #591 : Basic Geometry

If the perimeter of a rectangle is $\displaystyle 15$, and the width of the rectangle is $\displaystyle 3$, what is the area of the rectangle?

Possible Answers:

$\displaystyle 23$

$\displaystyle 22$

13.5 $\displaystyle 13.5$

23.5 $\displaystyle 23.5$

Correct answer:

13.5 $\displaystyle 13.5$

Explanation:

Recall how to find the perimeter of a rectangle:

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

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

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

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

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

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

Simplify.

$\text{length}=7.5-3$ $\displaystyle \text{length}=7.5-3$

Solve.

$\text{length}=4.5$ $\displaystyle \text{length}=4.5$

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

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

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

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

Solve.

$\text{Area}=13.5$ $\displaystyle \text{Area}=13.5$

Report an Error

Example Question #181 : Quadrilaterals

If the perimeter of a rectangle is 100 $\displaystyle 100$, and the width of the rectangle is $\displaystyle 12$, what is the area of the rectangle?

Possible Answers:

471 $\displaystyle 471$

546 $\displaystyle 546$

330 $\displaystyle 330$

456 $\displaystyle 456$

Correct answer:

456 $\displaystyle 456$

Explanation:

Recall how to find the perimeter of a rectangle:

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

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

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

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

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

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

Simplify.

$\text{length}=50-12$ $\displaystyle \text{length}=50-12$

Solve.

$\text{length}=38$ $\displaystyle \text{length}=38$

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

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

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

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

Solve.

$\text{Area}=456$ $\displaystyle \text{Area}=456$

Report an Error

Example Question #41 : How To Find The Area Of A Rectangle

If the perimeter of a rectangle is $\displaystyle 60$, and the width of the rectangle is $\displaystyle 12$, what is the area of the rectangle?

Possible Answers:

188 $\displaystyle 188$

216 $\displaystyle 216$

$\displaystyle 96$

112 $\displaystyle 112$

Correct answer:

216 $\displaystyle 216$

Explanation:

Recall how to find the perimeter of a rectangle:

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

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

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

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

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

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

Simplify.

$\text{length}=30-12$ $\displaystyle \text{length}=30-12$

Solve.

$\text{length}=18$ $\displaystyle \text{length}=18$

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

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

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

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

Solve.

$\text{Area}=216$ $\displaystyle \text{Area}=216$

Report an Error

Example Question #591 : Basic Geometry

If the perimeter of a rectangle is $\displaystyle 36$, and the width of the rectangle is $\displaystyle 9$, what is the area of the rectangle?

Possible Answers:

$\displaystyle 99$

$\displaystyle 81$

108 $\displaystyle 108$

$\displaystyle 90$

Correct answer:

$\displaystyle 81$

Explanation:

Recall how to find the perimeter of a rectangle:

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

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

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

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

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

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

Simplify.

$\text{length}=18-9$ $\displaystyle \text{length}=18-9$

Solve.

$\text{length}=9$ $\displaystyle \text{length}=9$

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

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

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

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

Solve.

$\text{Area}=81$ $\displaystyle \text{Area}=81$

Report an Error

Example Question #592 : Basic Geometry

If the perimeter of a rectangle is $\displaystyle 16$, and the width of the rectangle is $\displaystyle 7$, what is the area of the rectangle?

Possible Answers:

$\displaystyle 7$

$\displaystyle 12$

$\displaystyle 6$

$\displaystyle 15$

Correct answer:

$\displaystyle 7$

Explanation:

Recall how to find the perimeter of a rectangle:

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

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

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

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

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

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

Simplify.

$\text{length}=8-7$ $\displaystyle \text{length}=8-7$

Solve.

$\text{length}=1$ $\displaystyle \text{length}=1$

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

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

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

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

Solve.

$\text{Area}=7$ $\displaystyle \text{Area}=7$

Report an Error

Example Question #591 : Basic Geometry

If the perimeter of a rectangle is $\displaystyle 10$, and the width of the rectangle is $\displaystyle 1$, what is the area of the rectangle?

Possible Answers:

$\displaystyle 6$

$\displaystyle 3$

$\displaystyle 5$

$\displaystyle 4$

Correct answer:

$\displaystyle 4$

Explanation:

Recall how to find the perimeter of a rectangle:

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

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

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

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

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

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

Simplify.

$\text{length}=5-1$ $\displaystyle \text{length}=5-1$

Solve.

$\text{length}=4$ $\displaystyle \text{length}=4$

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

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

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

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

Solve.

$\text{Area}= 4$ $\displaystyle \text{Area}= 4$

Report an Error

Example Question #591 : Basic Geometry

If the perimeter of a rectangle is $\displaystyle 20$, and the width of the rectangle is $\displaystyle 9$, what is the area of the rectangle?

Possible Answers:

$\displaystyle 11$

$\displaystyle 8$

$\displaystyle 9$

$\displaystyle 10$

Correct answer:

$\displaystyle 9$

Explanation:

Recall how to find the perimeter of a rectangle:

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

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

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

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

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

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

Simplify.

$\text{length}=10-9$ $\displaystyle \text{length}=10-9$

Solve.

$\text{length}=1$ $\displaystyle \text{length}=1$

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

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

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

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

Solve.

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

Report an Error

Example Question #41 : How To Find The Area Of A Rectangle

If the perimeter of a rectangle is $\displaystyle 12$, and the width of the rectangle is $\displaystyle 1$, what is the area of the rectangle?

Possible Answers:

$\displaystyle 6$

$\displaystyle 7$

$\displaystyle 5$

$\displaystyle 4$

Correct answer:

$\displaystyle 5$

Explanation:

Recall how to find the perimeter of a rectangle:

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

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

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

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

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

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

Simplify.

$\text{length}=6-1$ $\displaystyle \text{length}=6-1$

Solve.

$\text{length}=5$ $\displaystyle \text{length}=5$

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

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

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

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

Solve.

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

Report an Error

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All Basic Geometry Resources

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #591 : Plane Geometry

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

Example Question #591 : Basic Geometry

Example Question #181 : Quadrilaterals

Example Question #41 : How To Find The Area Of A Rectangle

Example Question #591 : Basic Geometry

Example Question #592 : Basic Geometry

Example Question #591 : Basic Geometry

Example Question #591 : Basic Geometry

Example Question #41 : How To Find The Area Of A Rectangle

All Basic Geometry Resources

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