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Basic Geometry : Basic 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 #77 : How To Find The Area Of A Rectangle

If the radius of the circle is 7.2 , what is the area of the shaded region of the rectangle?

Possible Answers:

165.39

164.21

166.84

167.14

Correct answer:

167.14

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.

$\text{Area of circle}=\pi\times(7.2)^2$

$\text{Area of circle}=51.84\pi$

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.

$\text{Area of Rectangle}=15\times 22$

$\text{Area of Rectangle}=330$

Now, find the area of the shaded region.

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

$\text{Area of shaded region}=330-51.84\pi$

Solve and round to two decimal places.

$\text{Area of shaded region}=167.14$

Report an Error

Example Question #78 : How To Find The Area Of A Rectangle

A rectangle is placed inside a circle as shown in the figure.

If the diameter of the circle is , what is the area of the shaded region?

Possible Answers:

110.63

101.71

102.21

105.06

Correct answer:

105.06

Explanation:

In order to find the area of the shaded region, you must subtract the area of the rectangle from the area of the circle.

First, let's find the area of the circle.

Recall how to find the area of a circle:

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

Now, recall the relationship between the radius and the diameter.

$\text{radius}=\frac{\text{Diameter}}{2}$

Substitute in the length of the diameter to find the length of the radius.

$\text{radius}=\frac{16}{2}$

$\text{radius}=8$

Now, use the radius to find the area of the circle.

$\text{Area of circle}=\pi\times\text{8}^2$

$\text{Area of circle}=64\pi$

Next, find the area of the rectangle.

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

Substitute in the given values for the length and the width.

$\text{Area of rectangle}=12 \times 8$

$\text{Area of rectangle}=96$

Now that we have both areas, we can find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of circle}-\text{Area of rectangle}$

$\text{Area of shaded region}=64\pi - 96$

Solve and round the answer to two decimal places.

$\text{Area of shaded region}=105.06$

Report an Error

Example Question #221 : Quadrilaterals

A rectangle is placed inside a circle as shown in the figure.

If the diameter of the circle is , what is the area of the shaded region?

Possible Answers:

370.93

336.18

365.12

370.68

Correct answer:

370.93

Explanation:

In order to find the area of the shaded region, you must subtract the area of the rectangle from the area of the circle.

First, let's find the area of the circle.

Recall how to find the area of a circle:

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

Now, recall the relationship between the radius and the diameter.

$\text{radius}=\frac{\text{Diameter}}{2}$

Substitute in the length of the diameter to find the length of the radius.

$\text{radius}=\frac{26}{2}$

$\text{radius}=13$

Now, use the radius to find the area of the circle.

$\text{Area of circle}=\pi\times 13^2$

$\text{Area of circle}=169\pi$

Next, find the area of the rectangle.

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

Substitute in the given values for the length and the width.

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

$\text{Area of rectangle}=160$

Now that we have both areas, we can find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of circle}-\text{Area of rectangle}$

$\text{Area of shaded region}=169\pi - 160$

Solve and round the answer to two decimal places.

$\text{Area of shaded region}=370.93$

Report an Error

Example Question #631 : Basic Geometry

A rectangle is placed inside a circle as shown in the figure.

If the diameter of the circle is , what is the area of the shaded region?

Possible Answers:

268.30

227.13

229.87

220.36

Correct answer:

227.13

Explanation:

In order to find the area of the shaded region, you must subtract the area of the rectangle from the area of the circle.

First, let's find the area of the circle.

Recall how to find the area of a circle:

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

Now, recall the relationship between the radius and the diameter.

$\text{radius}=\frac{\text{Diameter}}{2}$

Substitute in the length of the diameter to find the length of the radius.

$\text{radius}=\frac{22}{2}$

$\text{radius}=11$

Now, use the radius to find the area of the circle.

$\text{Area of circle}=\pi\times11^2$

$\text{Area of circle}=121\pi$

Next, find the area of the rectangle.

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

Substitute in the given values for the length and the width.

$\text{Area of rectangle}=9\times 17$

$\text{Area of rectangle}=153$

Now that we have both areas, we can find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of circle}-\text{Area of rectangle}$

$\text{Area of shaded region}=121\pi - 153$

Solve and round the answer to two decimal places.

$\text{Area of shaded region}=227.13$

Report an Error

Example Question #632 : Basic Geometry

A rectangle is placed inside a circle as shown in the figure.

If the diameter of the circle is , what is the area of the shaded region?

Possible Answers:

82.06

81.03

83.66

84.69

Correct answer:

81.03

Explanation:

In order to find the area of the shaded region, you must subtract the area of the rectangle from the area of the circle.

First, let's find the area of the circle.

Recall how to find the area of a circle:

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

Now, recall the relationship between the radius and the diameter.

$\text{radius}=\frac{\text{Diameter}}{2}$

Substitute in the length of the diameter to find the length of the radius.

$\text{radius}=\frac{11}{2}$

Now, use the radius to find the area of the circle.

$\text{Area of circle}=\pi\times \left(\frac{11}{2}\right)^2$

$\text{Area of circle}=\frac{121}{4}\pi$

Next, find the area of the rectangle.

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

Substitute in the given values for the length and the width.

$\text{Area of rectangle}=2\times 7$

$\text{Area of rectangle}=14$

Now that we have both areas, we can find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of circle}-\text{Area of rectangle}$

$\text{Area of shaded region}=\frac{121}{4}\pi - 14$

Solve and round the answer to two decimal places.

$\text{Area of shaded region}=81.03$

Report an Error

Example Question #222 : Rectangles

A rectangle is placed inside a circle as shown in the figure.

If the diameter of the circle is , what is the area of the shaded region?

Possible Answers:

327.82

316.92

332.39

331.20

Correct answer:

332.39

Explanation:

In order to find the area of the shaded region, you must subtract the area of the rectangle from the area of the circle.

First, let's find the area of the circle.

Recall how to find the area of a circle:

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

Now, recall the relationship between the radius and the diameter.

$\text{radius}=\frac{\text{Diameter}}{2}$

Substitute in the length of the diameter to find the length of the radius.

$\text{radius}=\frac{24}{2}$

$\text{radius}=12$

Now, use the radius to find the area of the circle.

$\text{Area of circle}=\pi\times\text{12}^2$

$\text{Area of circle}=144\pi$

Next, find the area of the rectangle.

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

Substitute in the given values for the length and the width.

$\text{Area of rectangle}=15 \times 8$

$\text{Area of rectangle}=120$

Now that we have both areas, we can find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of circle}-\text{Area of rectangle}$

$\text{Area of shaded region}=144\pi - 120$

Solve and round the answer to two decimal places.

$\text{Area of shaded region}=332.39$

Report an Error

Example Question #83 : How To Find The Area Of A Rectangle

A rectangle is placed inside a circle as shown in the figure.

If the diameter of the circle is , what is the area of the shaded region?

Possible Answers:

22.22

25.27

26.34

21.58

Correct answer:

25.27

Explanation:

In order to find the area of the shaded region, you must subtract the area of the rectangle from the area of the circle.

First, let's find the area of the circle.

Recall how to find the area of a circle:

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

Now, recall the relationship between the radius and the diameter.

$\text{radius}=\frac{\text{Diameter}}{2}$

Substitute in the length of the diameter to find the length of the radius.

$\text{radius}=\frac{6}{2}$

$\text{radius}=3$

Now, use the radius to find the area of the circle.

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

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

Next, find the area of the rectangle.

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

Substitute in the given values for the length and the width.

$\text{Area of rectangle}=3\times 1$

$\text{Area of rectangle}=3$

Now that we have both areas, we can find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of circle}-\text{Area of rectangle}$

$\text{Area of shaded region}=9\pi - 3$

Solve and round the answer to two decimal places.

$\text{Area of shaded region}=25.27$

Report an Error

Example Question #84 : How To Find The Area Of A Rectangle

A rectangle is placed inside a circle as shown in the figure.

If the diameter of the circle is , what is the area of the shaded region?

Possible Answers:

34.48

30.06

39.87

36.32

Correct answer:

34.48

Explanation:

In order to find the area of the shaded region, you must subtract the area of the rectangle from the area of the circle.

First, let's find the area of the circle.

Recall how to find the area of a circle:

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

Now, recall the relationship between the radius and the diameter.

$\text{radius}=\frac{\text{Diameter}}{2}$

Substitute in the length of the diameter to find the length of the radius.

$\text{radius}=\frac{7}{2}$

Now, use the radius to find the area of the circle.

$\text{Area of circle}=\pi\times\left( \frac{7}{2}\right)^2$

$\text{Area of circle}=\frac{49}{4}\pi$

Next, find the area of the rectangle.

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

Substitute in the given values for the length and the width.

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

Now that we have both areas, we can find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of circle}-\text{Area of rectangle}$

$\text{Area of shaded region}=\frac{49}{4}\pi - 4$

Solve and round the answer to two decimal places.

$\text{Area of shaded region}=34.48$

Report an Error

Example Question #85 : How To Find The Area Of A Rectangle

A rectangle is placed inside a circle as shown in the figure.

If the diameter of the circle is , what is the area of the shaded region?

Possible Answers:

152.42

150.64

153.06

151.37

Correct answer:

153.06

Explanation:

In order to find the area of the shaded region, you must subtract the area of the rectangle from the area of the circle.

First, let's find the area of the circle.

Recall how to find the area of a circle:

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

Now, recall the relationship between the radius and the diameter.

$\text{radius}=\frac{\text{Diameter}}{2}$

Substitute in the length of the diameter to find the length of the radius.

$\text{radius}=\frac{16}{2}$

$\text{radius}=8$

Now, use the radius to find the area of the circle.

$\text{Area of circle}=\pi\times8^2$

$\text{Area of circle}=64\pi$

Next, find the area of the rectangle.

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

Substitute in the given values for the length and the width.

$\text{Area of rectangle}=4\times 12$

$\text{Area of rectangle}=48$

Now that we have both areas, we can find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of circle}-\text{Area of rectangle}$

$\text{Area of shaded region}=64\pi - 48$

Solve and round the answer to two decimal places.

$\text{Area of shaded region}=153.06$

Report an Error

Example Question #86 : How To Find The Area Of A Rectangle

A rectangle is placed inside a circle as shown in the figure.

If the diameter of the circle is , what is the area of the shaded region?

Possible Answers:

171.15

174.47

176.69

171.29

Correct answer:

174.47

Explanation:

In order to find the area of the shaded region, you must subtract the area of the rectangle from the area of the circle.

First, let's find the area of the circle.

Recall how to find the area of a circle:

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

Now, recall the relationship between the radius and the diameter.

$\text{radius}=\frac{\text{Diameter}}{2}$

Substitute in the length of the diameter to find the length of the radius.

$\text{radius}=\frac{18}{2}$

$\text{radius}=9$

Now, use the radius to find the area of the circle.

$\text{Area of circle}=\pi\times9^2$

$\text{Area of circle}=81\pi$

Next, find the area of the rectangle.

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

Substitute in the given values for the length and the width.

$\text{Area of rectangle}=5\times 16$

$\text{Area of rectangle}=80$

Now that we have both areas, we can find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of circle}-\text{Area of rectangle}$

$\text{Area of shaded region}=81\pi - 80$

Solve and round the answer to two decimal places.

$\text{Area of shaded region}=174.47$

Report an Error

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Basic Geometry : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #77 : How To Find The Area Of A Rectangle

Example Question #78 : How To Find The Area Of A Rectangle

Example Question #221 : Quadrilaterals

Example Question #631 : Basic Geometry

Example Question #632 : Basic Geometry

Example Question #222 : Rectangles

Example Question #83 : How To Find The Area Of A Rectangle

Example Question #84 : How To Find The Area Of A Rectangle

Example Question #85 : How To Find The Area Of A Rectangle

Example Question #86 : How To Find The Area Of A Rectangle

All Basic Geometry Resources

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