Basic Geometry : How to find the area of a right triangle

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #1453 : Basic Geometry

What is the area of a right triangle that has two side lengths of 7 and 8 inches respectively and the third side is the hypotenuse.

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a triangle is, .

In the case of a right triangle you can use the two side lengths other than the hypotenuse to solve the equation.

 

Area is in units squared.

Example Question #1454 : Basic Geometry

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,

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.

Example Question #1455 : Basic Geometry

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

1

Possible Answers:

Correct answer:

Explanation:

13

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:

Now, recall how to find the length of the radius from the length of the diameter.

Substitute in the given diameter to find the radius.

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

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

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

We can now find the area of the shaded region:

Solve and round to two decimal places.

 

Example Question #1456 : Basic Geometry

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

2

Possible Answers:

Correct answer:

Explanation:

13

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:

Now, recall how to find the length of the radius from the length of the diameter.

Substitute in the given diameter to find the radius.

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

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

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

We can now find the area of the shaded region:

Solve and round to two decimal places.

 

Example Question #1457 : Basic Geometry

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

3

Possible Answers:

Correct answer:

Explanation:

13

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:

Now, recall how to find the length of the radius from the length of the diameter.

Substitute in the given diameter to find the radius.

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

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

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

We can now find the area of the shaded region:

Solve and round to two decimal places.

 

Example Question #1458 : Basic Geometry

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

4

Possible Answers:

Correct answer:

Explanation:

13

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:

Now, recall how to find the length of the radius from the length of the diameter.

Substitute in the given diameter to find the radius.

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

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

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

We can now find the area of the shaded region:

Solve and round to two decimal places.

Example Question #1459 : Basic Geometry

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

5

Possible Answers:

Correct answer:

Explanation:

13

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:

Now, recall how to find the length of the radius from the length of the diameter.

Substitute in the given diameter to find the radius.

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

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

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

We can now find the area of the shaded region:

Solve and round to two decimal places.

Example Question #1460 : Basic Geometry

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

6

Possible Answers:

Correct answer:

Explanation:

13

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:

Now, recall how to find the length of the radius from the length of the diameter.

Substitute in the given diameter to find the radius.

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

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

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

We can now find the area of the shaded region:

Solve and round to two decimal places.

 

Example Question #471 : Triangles

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

7

Possible Answers:

Correct answer:

Explanation:

13

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:

Now, recall how to find the length of the radius from the length of the diameter.

Substitute in the given diameter to find the radius.

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

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

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

We can now find the area of the shaded region:

Solve and round to two decimal places.

 

Example Question #472 : Triangles

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

8

Possible Answers:

Correct answer:

Explanation:

13

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:

Now, recall how to find the length of the radius from the length of the diameter.

Substitute in the given diameter to find the radius.

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

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

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

We can now find the area of the shaded region:

Solve and round to two decimal places.

 

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