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

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Example Question #1 : How To Find The Area Of A Right Triangle

Righttriangle

Given:

A = 3 cm

B = 4 cm

What is the area of the right triangle ABC? 

Possible Answers:

7 square centimeters

5 square centimeters

12 square centimeters

13 square centimeters

6 square centimeters

Correct answer:

6 square centimeters

Explanation:

The area of a triangle is given by the equation:

Since the base leg of the given triangle is 4 cm, while the height is 3 cm, this gives:

Example Question #2 : How To Find The Area Of A Right Triangle

Righttriangle

Given:

A = 4 cm

B = 6 cm

What is the area of the right triangle ABC? 

Possible Answers:

24 square centimeters

10 square centimeters

12 square centimeters

11 square centimeters

8 square centimeters

Correct answer:

12 square centimeters

Explanation:

The area of a triangle is given by the equation:

Since the base leg of the given triangle is 4 cm, while the height is 3 cm, this gives:

Example Question #3 : How To Find The Area Of A Right Triangle

Righttriangle

Given:

A = 3 cm

B = 7 cm

What is the area of the triangle? 

Possible Answers:

7.6 square centimeters

8.3 square centimeters

10.5 square centimeters

10 square centimeters

7 square centimeters

Correct answer:

10.5 square centimeters

Explanation:

The area of a triangle is given by the equation:

Since the base leg of the given triangle is 4 cm, while the height is 3 cm, this gives:

Example Question #3 : How To Find The Area Of A Right Triangle

Righttriangle

Given that:

A = 6 cm

B = 10 cm

What is the area of the right trianlge ABC?

Possible Answers:

60 square centimeters

16 square centimeters

30 square centimeters

35 square centimeters

90 square centimeters

Correct answer:

30 square centimeters

Explanation:

The area of a triangle is given by the equation:

Since the base leg of the given triangle is 4 cm, while the height is 3 cm, this gives:

Example Question #4 : How To Find The Area Of A Right Triangle

Righttriangle

Given that:

A = 3 cm

B = 4 cm

C = 5 cm

What is the area of the right triangle ABC? 

Possible Answers:

10 square centimeters

12 square centimeters

6 square centimeters

6.5 square centimeters

7 square centimeters

Correct answer:

6 square centimeters

Explanation:

The area of a triangle is given by the equation:

Since the base leg of the given triangle is 4 cm, while the height is 3 cm, this gives:

Example Question #6 : How To Find The Area Of A Right Triangle

Righttriangle

Given that:

A = 10 cm 

B = 20 cm

What is the area of the right triangle ABC?

Possible Answers:

120 square centimeters

30 square centimeters

100 square centimeters

70 square centimeters

50 square centimeters

Correct answer:

100 square centimeters

Explanation:

The area of a triangle is given by the equation:

Since the base leg of the given triangle is 4 cm, while the height is 3 cm, this gives:

Example Question #1 : How To Find The Area Of A Right Triangle

The length of the legs of the triangle below (not to scale) are as follows:

 cm

 cm

Right_triangle_with_labeled_sides 

What is the area of the triangle?

Possible Answers:

 linear centimeters

 square centimeters

 square centimeters

 square centimeters

 square centimeters

Correct answer:

 square centimeters

Explanation:

The formula for the area of a triangle is

 

where  is the base of the triangle and  is the height.

For the triangle shown, side  is the base and side  is the height.

Therefore, the area is equal to

 

or, based on the units given, 42 square centimeters

Example Question #1 : How To Find The Area Of A Right Triangle

An equilateral triangle has a side of

What is the area of the triangle?

Possible Answers:

Correct answer:

Explanation:

An equilateral triangle has three congruent sides. The area of a triangle is given by where is the base and is the height.

The equilateral triangle can be broken into two right triangles, where the legs are and and the hypotenuses is .

Using the Pythagorean Theorem we get or and the area is

Example Question #2 : How To Find The Area Of A Right Triangle

The hypotenuse of a  triangle measures eight inches. What is the area of this triangle (radical form, if applicable)?

Possible Answers:

It is impossible to tell from the information given.

Correct answer:

Explanation:

In a , the shorter leg is half as long as the hypotenuse, and the longer leg is  times the length of the shorter. Since the hypotenuse is 8, the shorter leg is 4, and the longer leg is , making the area:

Example Question #8 : How To Find The Area Of A Right Triangle

Img052

Possible Answers:

Correct answer:

Explanation:

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