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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 #478 : Triangles

The diameter of the circle is 3.2 , what is the area of the shaded region?

Possible Answers:

49.71

49.96

50.95

45.09

Correct answer:

49.96

Explanation:

To find the area of the shaded region, we will first need to find the area of the right triangle and 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 how to find the length of the radius from the length of the diameter.

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

Substitute in the given diameter to find the radius.

$\text{Radius}=\frac{3.2}{2}$

$\text{Radius}=1.6$

Now, substitute in the radius to find the area of the circle.

$\text{Area of Circle}=\pi\times 1.6^2$

$\text{Area of Circle}=2.56\pi$

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

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

Substitute in the given base and height to find the area.

$\text{Area of Triangle}=\frac{4 \times 29}{2}$

$\text{Area of Triangle}=58$

We can now find the area of the shaded region:

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

$\text{Area of Shaded Region}=58-2.56\pi$

Solve and round to two decimal places.

$\text{Area of Shaded Region}=49.96$

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Example Question #281 : Right Triangles

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

Possible Answers:

110.95

111.09

113.46

112.45

Correct answer:

113.46

Explanation:

To find the area of the shaded region, we will first need to find the area of the right triangle and 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 how to find the length of the radius from the length of the diameter.

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

Substitute in the given diameter to find the radius.

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

$\text{Radius}=5$

Now, substitute in the radius to find the area of the circle.

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

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

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

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

Substitute in the given base and height to find the area.

$\text{Area of Triangle}=\frac{12 \times 32}{2}$

$\text{Area of Triangle}=192$

We can now find the area of the shaded region:

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

$\text{Area of Shaded Region}=192-25\pi$

Solve and round to two decimal places.

$\text{Area of Shaded Region}=113.46$

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Example Question #81 : How To Find The Area Of A Right Triangle

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

Possible Answers:

34.12

34.37

35.98

33.06

Correct answer:

34.37

Explanation:

To find the area of the shaded region, we will first need to find the area of the right triangle and 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 how to find the length of the radius from the length of the diameter.

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

Substitute in the given diameter to find the radius.

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

Now, substitute in the radius to find the area of the circle.

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

$\text{Area of Circle}=\frac{25}{4}\pi$

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

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

Substitute in the given base and height to find the area.

$\text{Area of Triangle}=\frac{6 \times 18}{2}$

$\text{Area of Triangle}=54$

We can now find the area of the shaded region:

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

$\text{Area of Shaded Region}=54-\frac{25}{4}\pi$

Solve and round to two decimal places.

$\text{Area of Shaded Region}=34.37$

Report an Error

Example Question #81 : How To Find The Area Of A Right Triangle

The diameter of the circle is , find the area of the shaded region.

Possible Answers:

13.38

9.98

12.41

10.99

Correct answer:

13.38

Explanation:

To find the area of the shaded region, we will first need to find the area of the right triangle and 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 how to find the length of the radius from the length of the diameter.

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

Substitute in the given diameter to find the radius.

$\text{Radius}=\frac{9}{2}$

Now, substitute in the radius to find the area of the circle.

$\text{Area of Circle}=\pi\times\left( \frac{9}{2}\right)^2$

$\text{Area of Circle}=\frac{81}{4}\pi$

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

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

Substitute in the given base and height to find the area.

$\text{Area of Triangle}=\frac{11 \times 14}{2}$

$\text{Area of Triangle}=77$

We can now find the area of the shaded region:

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

$\text{Area of Shaded Region}=77-\frac{81}{4}\pi$

Solve and round to two decimal places.

$\text{Area of Shaded Region}=13.38$

Report an Error

Example Question #82 : How To Find The Area Of A Right Triangle

The diameter of the circle is 2.2 , find the area of the shaded region.

Possible Answers:

17.78

15.98

16.20

14.28

Correct answer:

16.20

Explanation:

To find the area of the shaded region, we will first need to find the area of the right triangle and 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 how to find the length of the radius from the length of the diameter.

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

Substitute in the given diameter to find the radius.

$\text{Radius}=\frac{2.2}{2}$

$\text{Radius}=1.1$

Now, substitute in the radius to find the area of the circle.

$\text{Area of Circle}=\pi\times 1.1^2$

$\text{Area of Circle}=1.21\pi$

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

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

Substitute in the given base and height to find the area.

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

$\text{Area of Triangle}=20$

We can now find the area of the shaded region:

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

$\text{Area of Shaded Region}=20-1.21\pi$

Solve and round to two decimal places.

$\text{Area of Shaded Region}=16.20$

Report an Error

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

The diameter of the circle is , find the area of the shaded region.

Possible Answers:

89.89

93.44

90.90

91.28

Correct answer:

90.90

Explanation:

To find the area of the shaded region, we will first need to find the area of the right triangle and 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 how to find the length of the radius from the length of the diameter.

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

Substitute in the given diameter to find the radius.

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

$\text{Radius}=6$

Now, substitute in the radius to find the area of the circle.

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

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

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

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

Substitute in the given base and height to find the area.

$\text{Area of Triangle}=\frac{17 \times 24}{2}$

$\text{Area of Triangle}=204$

We can now find the area of the shaded region:

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

$\text{Area of Shaded Region}=204-36\pi$

Solve and round to two decimal places.

$\text{Area of Shaded Region}=90.90$

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Example Question #1461 : Plane Geometry

A triangle has a height of 5 inches and a base of 10 inches. What is the area of this triangle?

Possible Answers:

A=65in^2

A=30in^2

A=15in^2

A=25in^2

None of these.

Correct answer:

A=25in^2

Explanation:

The area of a right triangle can be found by A=.5bh .

$A=.5bh=.5(10)(5)=\mathbf{25in^2}$

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Example Question #82 : How To Find The Area Of A Right Triangle

Prblem 6 basic geometry

Triangle ABC has the given side lengths. Find the area of triangle ABC.

Possible Answers:

$121\ inches^2$

$100\ inches^2$

$182\ inches^2$

$91\ inches^2$

$89\ inches^2$

Correct answer:

$91\ inches^2$

Explanation:

Imagine a right triangle as a square cut in half at a diagonal angle.

When figuring out the area, you figure it out the same way as finding the area of a square, but after multiplying length x width, divide the answer by 2.

$14 \cdot 13 = 182inches^2$

182/2=91 inches^2

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Example Question #87 : How To Find The Area Of A Right Triangle

Find the area, , of a right triangle XYZ whose sides are X=12 , Y=5 , Z=13 .

Possible Answers:

A=35

A=50

A=30

A=40

Correct answer:

A=30

Explanation:

The formula for the area of a right triangle is

$A=\frac{1}{2}XY$ .

Plugging in the values given,

$A=\frac{1}{2}*5*12=30$ .

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

Shape area right triangle

In the right triangle shown here, a=5 and b=12 . What is its area in square units?

Possible Answers:

Correct answer:

Explanation:

The area of a right triangle is given by $A=\frac{bh}{2}$ , where represents the length of the triangle's base and represents the length of the triangle's height. The base and the height of the triangle given in the problem are and units long, respectively. Hence, the area of the triangle can be calculated as follows:

$A=\frac{bh}{2}= \frac{(12)(5)}{2} = 30$ .

Hence, the area of a right triangle with base length units and height units is square units.

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #478 : Triangles

Example Question #281 : Right Triangles

Example Question #81 : How To Find The Area Of A Right Triangle

Example Question #81 : How To Find The Area Of A Right Triangle

Example Question #82 : How To Find The Area Of A Right Triangle

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

Example Question #1461 : Plane Geometry

Example Question #82 : How To Find The Area Of A Right Triangle

Example Question #87 : How To Find The Area Of A Right Triangle

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

All Basic Geometry Resources

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