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Basic Geometry : Triangles

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Example Questions

Example Question #471 : Triangles

Find the area of a right triangle with base 4 and height 5.

Possible Answers:

Correct answer:

Explanation:

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

$A=\frac{1}{2}Bh=\frac{1}{2}*4*5=10$

If the formula escapes you, simply remember that two equivalent triangles put together equal a rectangle. So, the area of a triangle must be half the area of a rectangle.

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Example Question #472 : Triangles

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

Possible Answers:

19.21

21.28

20.09

20.86

Correct answer:

20.86

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.

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

$\text{Radius}=1$

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

$\text{Area of Circle}=\pi\times 1^2$

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

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.

$\text{Area of Triangle}=\frac{4 \times 12}{2}$

$\text{Area of Triangle}=24$

We can now find the area of the shaded region:

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

$\text{Area of Shaded Region}=24-\pi$

Solve and round to two decimal places.

$\text{Area of Shaded Region}=20.86$

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Example Question #473 : Triangles

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

Possible Answers:

13.04

11.82

12.48

12.93

Correct answer:

12.93

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.

$\text{Radius}=\frac{3}{2}$

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

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

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

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.

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

$\text{Area of Triangle}=20$

We can now find the area of the shaded region:

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

$\text{Area of Shaded Region}=20-\frac{9}{4}\pi$

Solve and round to two decimal places.

$\text{Area of Shaded Region}=12.93$

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Example Question #474 : Triangles

The diameter of the circle is 1.2 , find the area of the shaded region.

Possible Answers:

14.90

12.13

13.87

10.71

Correct answer:

13.87

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.

$\text{Radius}=\frac{1.2}{2}$

$\text{Radius}=0.6$

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

$\text{Area of Circle}=\pi\times 0.6^2$

$\text{Area of Circle}=0.36\pi$

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.

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

$\text{Area of Triangle}=15$

We can now find the area of the shaded region:

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

$\text{Area of Shaded Region}=15-0.36\pi$

Solve and round to two decimal places.

$\text{Area of Shaded Region}=13.87$

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Example Question #475 : Triangles

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

Possible Answers:

39.73

38.71

42.51

40.82

Correct answer:

39.73

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.

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

$\text{Radius}=3$

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

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

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

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.

$\text{Area of Triangle}=\frac{8 \times 17}{2}$

$\text{Area of Triangle}=68$

We can now find the area of the shaded region:

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

$\text{Area of Shaded Region}=68-9\pi$

Solve and round to two decimal places.

$\text{Area of Shaded Region}=39.73$

Report an Error

Example Question #476 : Triangles

The diameter of the circle is 6.2 , what is the area of the shaded region?

Possible Answers:

16.89

15.00

18.45

17.81

Correct answer:

17.81

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.

$\text{Radius}=\frac{6.2}{2}$

$\text{Radius}=3.1$

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

$\text{Area of Circle}=\pi\times 3.1^2$

$\text{Area of Circle}=9.61\pi$

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.

$\text{Area of Triangle}=\frac{8 \times 12}{2}$

$\text{Area of Triangle}=48$

We can now find the area of the shaded region:

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

$\text{Area of Shaded Region}=48-9.61\pi$

Solve and round to two decimal places.

$\text{Area of Shaded Region}=17.81$

Report an Error

Example Question #477 : Triangles

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

Possible Answers:

13.82

14.44

14.60

12.73

Correct answer:

12.73

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.

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

$\text{Radius}=4$

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

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

$\text{Area of Circle}=16\pi$

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.

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

$\text{Area of Triangle}=63$

We can now find the area of the shaded region:

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

$\text{Area of Shaded Region}=63-16\pi$

Solve and round to two decimal places.

$\text{Area of Shaded Region}=12.73$

Report an Error

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.

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

Report an Error

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.

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

Report an Error

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

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Basic Geometry : Triangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #471 : Triangles

Example Question #472 : Triangles

Example Question #473 : Triangles

Example Question #474 : Triangles

Example Question #475 : Triangles

Example Question #476 : Triangles

Example Question #477 : Triangles

Example Question #478 : Triangles

Example Question #281 : Right Triangles

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

All Basic Geometry Resources

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