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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 #131 : Circles

Find the area of a circle given radius is 1.

Possible Answers:

$4\pi$

$2\pi$

$\pi$

$\pi^2$

Correct answer:

$\pi$

Explanation:

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

$A=\pi{r^2}=\pi*1^2=\pi$

The trick with this problem is to remember that squaring 1 does not change its value. Some students often struggle with that concept and just trusting that the answer is one, but just trust the formula and you will get the right answer.

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Example Question #132 : Basic Geometry

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

Possible Answers:

33.92

34.27

31.54

32.08

Correct answer:

34.27

Explanation:

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

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.

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

Plug in the value of the diameter to find the value of the radius.

$\text{Radius}=\frac{8}{2}=4$

Now, plug in the value of the radius in to find the area of the circle.

$\text{Area of Circle}=\pi\times 4^2=16\pi$

Next, recall how to find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times\text{height}}{2}$

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

$\text{Area of Triangle}=\frac{4 \times 8}{2}=16$

We are now ready to find the area of the shaded region.

$\text{Area of Shaded Region}=\text{Area of Circle}-\text{Area of Triangle}$

$\text{Area of Shaded Region}=16\pi-16=34.27$

Remember to round to decimal places.

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Example Question #133 : Basic Geometry

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

Possible Answers:

50.06

53.97

58.54

54.21

Correct answer:

58.54

Explanation:

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

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.

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

Plug in the value of the diameter to find the value of the radius.

$\text{Radius}=\frac{10}{2}=5$

Now, plug in the value of the radius in to find the area of the circle.

$\text{Area of Circle}=\pi\times 5^2=25\pi$

Next, recall how to find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times\text{height}}{2}$

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

$\text{Area of Triangle}=\frac{4 \times 10}{2}=20$

We are now ready to find the area of the shaded region.

$\text{Area of Shaded Region}=\text{Area of Circle}-\text{Area of Triangle}$

$\text{Area of Shaded Region}=25\pi-20=58.54$

Remember to round to decimal places.

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Example Question #134 : Basic Geometry

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

Possible Answers:

531.09

557.98

564.25

579.51

Correct answer:

564.25

Explanation:

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

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.

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

Plug in the value of the diameter to find the value of the radius.

$\text{Radius}=\frac{32}{2}=16$

Now, plug in the value of the radius in to find the area of the circle.

$\text{Area of Circle}=\pi\times 17^2=256\pi$

Next, recall how to find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times\text{height}}{2}$

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

$\text{Area of Triangle}=\frac{32 \times 15}{2}=240$

We are now ready to find the area of the shaded region.

$\text{Area of Shaded Region}=\text{Area of Circle}-\text{Area of Triangle}$

$\text{Area of Shaded Region}=256\pi-240=564.25$

Remember to round to decimal places.

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Example Question #132 : Circles

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

Possible Answers:

90.94

95.63

89.50

92.67

Correct answer:

90.94

Explanation:

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

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.

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

Plug in the value of the diameter to find the value of the radius.

$\text{Radius}=\frac{14}{2}=7$

Now, plug in the value of the radius in to find the area of the circle.

$\text{Area of Circle}=\pi\times 7^2=49\pi$

Next, recall how to find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times\text{height}}{2}$

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

$\text{Area of Triangle}=\frac{14 \times 9}{2}=63$

We are now ready to find the area of the shaded region.

$\text{Area of Shaded Region}=\text{Area of Circle}-\text{Area of Triangle}$

$\text{Area of Shaded Region}=49\pi-63=90.94$

Remember to round to decimal places.

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Example Question #136 : Basic Geometry

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

Possible Answers:

507.29

509.67

505.38

511.86

Correct answer:

511.86

Explanation:

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

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.

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

Plug in the value of the diameter to find the value of the radius.

$\text{Radius}=\frac{30}{2}=15$

Now, plug in the value of the radius in to find the area of the circle.

$\text{Area of Circle}=\pi\times 15^2=225\pi$

Next, recall how to find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times\text{height}}{2}$

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

$\text{Area of Triangle}=\frac{30 \times 13}{2}=195$

We are now ready to find the area of the shaded region.

$\text{Area of Shaded Region}=\text{Area of Circle}-\text{Area of Triangle}$

$\text{Area of Shaded Region}=225\pi-195=511.86$

Remember to round to decimal places.

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Example Question #137 : Basic Geometry

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

Possible Answers:

282.37

281.05

289.61

284.39

Correct answer:

284.39

Explanation:

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

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.

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

Plug in the value of the diameter to find the value of the radius.

$\text{Radius}=\frac{24}{2}=12$

Now, plug in the value of the radius in to find the area of the circle.

$\text{Area of Circle}=\pi\times 12^2=144\pi$

Next, recall how to find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times\text{height}}{2}$

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

$\text{Area of Triangle}=\frac{24 \times 14}{2}=168$

We are now ready to find the area of the shaded region.

$\text{Area of Shaded Region}=\text{Area of Circle}-\text{Area of Triangle}$

$\text{Area of Shaded Region}=144\pi-168=284.39$

Remember to round to decimal places.

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Example Question #132 : Basic Geometry

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

Possible Answers:

632.87

635.92

631.50

669.48

Correct answer:

635.92

Explanation:

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

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.

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

Plug in the value of the diameter to find the value of the radius.

$\text{Radius}=\frac{34}{2}=17$

Now, plug in the value of the radius in to find the area of the circle.

$\text{Area of Circle}=\pi\times 17^2=289\pi$

Next, recall how to find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times\text{height}}{2}$

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

$\text{Area of Triangle}=\frac{34 \times 16}{2}=272$

We are now ready to find the area of the shaded region.

$\text{Area of Shaded Region}=\text{Area of Circle}-\text{Area of Triangle}$

$\text{Area of Shaded Region}=289\pi-272=635.92$

Remember to round to decimal places.

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Example Question #139 : Basic Geometry

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

Possible Answers:

651.28

689.36

657.88

662.73

Correct answer:

657.88

Explanation:

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

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.

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

Plug in the value of the diameter to find the value of the radius.

$\text{Radius}=\frac{36}{2}=18$

Now, plug in the value of the radius in to find the area of the circle.

$\text{Area of Circle}=\pi\times 18^2=324\pi$

Next, recall how to find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times\text{height}}{2}$

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

$\text{Area of Triangle}=\frac{36 \times 20}{2}=360$

We are now ready to find the area of the shaded region.

$\text{Area of Shaded Region}=\text{Area of Circle}-\text{Area of Triangle}$

$\text{Area of Shaded Region}=324\pi-360=657.88$

Remember to round to decimal places.

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Example Question #140 : Basic Geometry

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

Possible Answers:

72.51

73.33

71.10

69.50

Correct answer:

71.10

Explanation:

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

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.

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

Plug in the value of the diameter to find the value of the radius.

$\text{Radius}=\frac{12}{2}=6$

Now, plug in the value of the radius in to find the area of the circle.

$\text{Area of Circle}=\pi\times 6^2=36\pi$

Next, recall how to find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times\text{height}}{2}$

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

$\text{Area of Triangle}=\frac{12 \times 7}{2}=42$

We are now ready to find the area of the shaded region.

$\text{Area of Shaded Region}=\text{Area of Circle}-\text{Area of Triangle}$

$\text{Area of Shaded Region}=36\pi-42=71.10$

Remember to round to decimal places.

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #131 : Circles

Example Question #132 : Basic Geometry

Example Question #133 : Basic Geometry

Example Question #134 : Basic Geometry

Example Question #132 : Circles

Example Question #136 : Basic Geometry

Example Question #137 : Basic Geometry

Example Question #132 : Basic Geometry

Example Question #139 : Basic Geometry

Example Question #140 : Basic Geometry

All Basic Geometry Resources

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