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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 #61 : How To Find The Area Of A Rectangle

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

Possible Answers:

398.74

336.90

365.21

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.

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

Report an Error

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 #211 : Rectangles

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

Possible Answers:

21.69

20.79

21.99

20.54

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.

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

Report an Error

Example Question #62 : How To Find The Area Of A Rectangle

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

Possible Answers:

31.02

37.15

32.43

33.69

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

Example Question #75 : How To Find The Area Of A Rectangle

If the radius of the circle is 3.9 , what is the area of the shaded region of the rectangle?

Possible Answers:

112.44

112.22

112.65

112.87

Correct answer:

112.22

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.

$\text{Area of circle}=\pi\times(3.9)^2$

$\text{Area of circle}=15.21\pi$

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.

$\text{Area of Rectangle}=8\times 20$

$\text{Area of Rectangle}=160$

Now, find the area of the shaded region.

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

$\text{Area of shaded region}=160-15.21\pi$

Solve and round to two decimal places.

$\text{Area of shaded region}=112.22$

Report an Error

Example Question #76 : How To Find The Area Of A Rectangle

If the radius of the circle is 3.8 , what is the area of the shaded region of the rectangle?

Possible Answers:

124.98

130.64

125.78

135.00

Correct answer:

130.64

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.

$\text{Area of circle}=\pi\times(3.8)^2$

$\text{Area of circle}=14.44\pi$

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.

$\text{Area of Rectangle}=8\times 22$

$\text{Area of Rectangle}=176$

Now, find the area of the shaded region.

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

$\text{Area of shaded region}=176-14.44\pi$

Solve and round to two decimal places.

$\text{Area of shaded region}=130.64$

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 #61 : How To Find The Area Of A Rectangle

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

Example Question #211 : Rectangles

Example Question #62 : How To Find The Area Of A Rectangle

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

Example Question #75 : How To Find The Area Of A Rectangle

Example Question #76 : How To Find The Area Of A Rectangle

All Basic Geometry Resources

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