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Basic Geometry : Rectangles

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 #211 : Quadrilaterals

Find the area of a rectangle given length 7 and width 2.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the area of a rectangle. Thus,

A=l*w=7*2=14

If you forget the formula, simply imagine you have two rows of blocks with 7 in them each. If you count the total number of blocks you have, you will realize you have 14!

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Example Question #619 : Basic Geometry

If the radius of the circle is , find the area of the shaded region of the rectangle.

Possible Answers:

201.32

202.28

209.46

208.64

Correct answer:

209.46

Explanation:

In order to find the area of the shaded region, we will need to subtract the area of the circle from the area of the rectangle.

Let's start by finding the area of a circle. Recall the formula to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Substitute in the value of the radius, which is given by the question.

$\text{Area of circle}=\pi\times(5)^2$

$\text{Area of circle}=25\pi$

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

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

Substitute in the values given by the figure to find the area of the rectangle.

$\text{Area of Rectangle}=12 \times 24$

$\text{Area of Rectangle} =288$

Now, find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of Rectangle}-\text{Area of Circle}$

$\text{Area of shaded region}=288-25\pi$

Solve and round to two decimal places.

$\text{Area of shaded region}=209.46$

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Example Question #212 : Quadrilaterals

If the radius of the circle is , find the area of the shaded region of the rectangle.

Possible Answers:

398.74

365.21

336.90

373.24

Correct answer:

336.90

Explanation:

In order to find the area of the shaded region, we will need to subtract the area of the circle from the area of the rectangle.

Let's start by finding the area of a circle. Recall the formula to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Substitute in the value of the radius, which is given by the question.

$\text{Area of circle}=\pi\times(6)^2$

$\text{Area of circle}=36\pi$

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

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

Substitute in the values given by the figure to find the area of the rectangle.

$\text{Area of Rectangle}=15 \times 30$

$\text{Area of Rectangle}=450$

Now, find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of Rectangle}-\text{Area of Circle}$

$\text{Area of shaded region}=450-36\pi$

Solve and round to two decimal places.

$\text{Area of shaded region}=336.90$

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Example Question #64 : How To Find The Area Of A Rectangle

If the radius of the circle is $\frac{2}{3}$ , what is the area of the shaded region of the rectangle?

Possible Answers:

17.50

16.33

16.98

16.60

Correct answer:

16.60

Explanation:

In order to find the area of the shaded region, we will need to subtract the area of the circle from the area of the rectangle.

Let's start by finding the area of a circle. Recall the formula to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Substitute in the value of the radius, which is given by the question.

$\text{Area of circle}=\pi\times\left(\frac{2}{3}\right)^2$

$\text{Area of circle}=\frac{4}{9}\pi$

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

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

Substitute in the values given by the figure to find the area of the rectangle.

$\text{Area of Rectangle}=3\times 6$

$\text{Area of Rectangle}=18$

Now, find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of Rectangle}-\text{Area of Circle}$

$\text{Area of shaded region}=18-\frac{4}{9}\pi$

Solve and round to two decimal places.

$\text{Area of shaded region}=16.60$

Report an Error

Example Question #213 : Quadrilaterals

If the radius of the circle is 1.3 , what is the area of the shaded region of the rectangle?

Possible Answers:

21.69

20.54

21.99

20.79

Correct answer:

21.69

Explanation:

In order to find the area of the shaded region, we will need to subtract the area of the circle from the area of the rectangle.

Let's start by finding the area of a circle. Recall the formula to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Substitute in the value of the radius, which is given by the question.

$\text{Area of circle}=\pi\times(1.3)^2$

$\text{Area of circle}=1.69\pi$

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

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

Substitute in the values given by the figure to find the area of the rectangle.

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

$\text{Area of Rectangle}=27$

Now, find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of Rectangle}-\text{Area of Circle}$

$\text{Area of shaded region}=27-1.69\pi$

Solve and round to two decimal places.

$\text{Area of shaded region}=21.69$

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Example Question #214 : Quadrilaterals

If the radius of the circle is , what is the area of the shaded region of the rectangle?

Possible Answers:

32.43

31.02

33.69

37.15

Correct answer:

32.43

Explanation:

In order to find the area of the shaded region, we will need to subtract the area of the circle from the area of the rectangle.

Let's start by finding the area of a circle. Recall the formula to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Substitute in the value of the radius, which is given by the question.

$\text{Area of circle}=\pi\times(2)^2$

$\text{Area of circle}=4\pi$

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

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

Substitute in the values given by the figure to find the area of the rectangle.

$\text{Area of Rectangle}=5\times 9$

$\text{Area of Rectangle}=45$

Now, find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of Rectangle}-\text{Area of Circle}$

$\text{Area of shaded region}=45-4\pi$

Solve and round to two decimal places.

$\text{Area of shaded region}=32.43$

Report an Error

Example Question #71 : How To Find The Area Of A Rectangle

If the radius of the circle is 3.2 , what is the area of the shaded region of the rectangle?

Possible Answers:

70.67

74.89

72.83

71.54

Correct answer:

72.83

Explanation:

In order to find the area of the shaded region, we will need to subtract the area of the circle from the area of the rectangle.

Let's start by finding the area of a circle. Recall the formula to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Substitute in the value of the radius, which is given by the question.

$\text{Area of circle}=\pi\times(3.2)^2$

$\text{Area of circle}=10.24\pi$

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

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

Substitute in the values given by the figure to find the area of the rectangle.

$\text{Area of Rectangle}=7\times 15$

$\text{Area of Rectangle}=105$

Now, find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of Rectangle}-\text{Area of Circle}$

$\text{Area of shaded region}=105-10.24\pi$

Solve and round to two decimal places.

$\text{Area of shaded region}=72.83$

Report an Error

Example Question #623 : Plane Geometry

If the radius of the circle is , what is the area of the shaded region of the rectangle?

Possible Answers:

83.73

80.05

81.11

84.69

Correct answer:

83.73

Explanation:

In order to find the area of the shaded region, we will need to subtract the area of the circle from the area of the rectangle.

Let's start by finding the area of a circle. Recall the formula to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Substitute in the value of the radius, which is given by the question.

$\text{Area of circle}=\pi\times(3)^2$

$\text{Area of circle}=9\pi$

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

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

Substitute in the values given by the figure to find the area of the rectangle.

$\text{Area of Rectangle}=7\times 16$

$\text{Area of Rectangle}=112$

Now, find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of Rectangle}-\text{Area of Circle}$

$\text{Area of shaded region}=112-9\pi$

Solve and round to two decimal places.

$\text{Area of shaded region}=83.73$

Report an Error

Example Question #73 : How To Find The Area Of A Rectangle

If the radius of the circle is $\frac{3}{4}$ , find the area of the shaded region of the rectangle.

Possible Answers:

14.23

11.22

13.97

12.68

Correct answer:

14.23

Explanation:

In order to find the area of the shaded region, we will need to subtract the area of the circle from the area of the rectangle.

Let's start by finding the area of a circle. Recall the formula to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Substitute in the value of the radius, which is given by the question.

$\text{Area of circle}=\pi\times\left(\frac{3}{4} \right) ^2$

$\text{Area of circle}=\frac{9}{16}\pi$

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

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

Substitute in the values given by the figure to find the area of the rectangle.

$\text{Area of Rectangle}=2\times 8$

$\text{Area of Rectangle}=16$

Now, find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of Rectangle}-\text{Area of Circle}$

$\text{Area of shaded region}=16-\frac{9}{16}\pi$

Solve and round to two decimal places.

$\text{Area of shaded region}=14.23$

Report an Error

Example Question #74 : How To Find The Area Of A Rectangle

If the radius of the circle is 3.75 , what is the area of the shaded region of the rectangle?

Possible Answers:

89.66

81.64

83.82

85.47

Correct answer:

83.82

Explanation:

In order to find the area of the shaded region, we will need to subtract the area of the circle from the area of the rectangle.

Let's start by finding the area of a circle. Recall the formula to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Substitute in the value of the radius, which is given by the question.

$\text{Area of circle}=\pi\times(3.75)^2$

$\text{Area of circle}=14.0625\pi$

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

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

Substitute in the values given by the figure to find the area of the rectangle.

$\text{Area of Rectangle}=8\times 16$

$\text{Area of Rectangle}=128$

Now, find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of Rectangle}-\text{Area of Circle}$

$\text{Area of shaded region}=128-14.0625\pi$

Solve and round to two decimal places.

$\text{Area of shaded region}=83.82$

Report an Error

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Basic Geometry : Rectangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #211 : Quadrilaterals

Example Question #619 : Basic Geometry

Example Question #212 : Quadrilaterals

Example Question #64 : How To Find The Area Of A Rectangle

Example Question #213 : Quadrilaterals

Example Question #214 : Quadrilaterals

Example Question #71 : How To Find The Area Of A Rectangle

Example Question #623 : Plane Geometry

Example Question #73 : How To Find The Area Of A Rectangle

Example Question #74 : How To Find The Area Of A Rectangle

All Basic Geometry Resources

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