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

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Example Questions

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:

13 square centimeters

6 square centimeters

12 square centimeters

7 square centimeters

5 square centimeters

Correct answer:

6 square centimeters

Explanation:

The area of a triangle is given by the equation:

$A_{\Delta } = (1/2)*(base)*(height)$

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

$A_{\Delta }=(1/2)*3*4 = 6 cm^{2}$

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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:

10 square centimeters

11 square centimeters

12 square centimeters

8 square centimeters

24 square centimeters

Correct answer:

12 square centimeters

Explanation:

The area of a triangle is given by the equation:

$A_{\Delta } = (1/2)*(base)*(height)$

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

$A_{\Delta }=(1/2)*4*6 = 12 cm^{2}$

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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:

8.3 square centimeters

10 square centimeters

7 square centimeters

10.5 square centimeters

7.6 square centimeters

Correct answer:

10.5 square centimeters

Explanation:

The area of a triangle is given by the equation:

$A_{\Delta } = (1/2)*(base)*(height)$

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

$A_{\Delta }=(1/2)*3*7 = 10.5 cm^{2}$

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Example Question #4 : 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

30 square centimeters

90 square centimeters

35 square centimeters

16 square centimeters

Correct answer:

30 square centimeters

Explanation:

The area of a triangle is given by the equation:

$A_{\Delta } = (1/2)*(base)*(height)$

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

$A_{\Delta }=(1/2)*10*6 = 12 cm^{2}$

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Example Question #1 : 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:

6.5 square centimeters

12 square centimeters

7 square centimeters

6 square centimeters

10 square centimeters

Correct answer:

6 square centimeters

Explanation:

The area of a triangle is given by the equation:

$A_{\Delta } = (1/2)*(base)*(height)$

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

$A_{\Delta }=(1/2)*4*3 = 6 cm^{2}$

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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:

100 square centimeters

30 square centimeters

70 square centimeters

50 square centimeters

120 square centimeters

Correct answer:

100 square centimeters

Explanation:

The area of a triangle is given by the equation:

$A_{\Delta } = (1/2)*(base)*(height)$

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

$A_{\Delta }=(1/2)*20*10 = 100 cm^{2}$

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Example Question #7 : How To Find The Area Of A Right Triangle

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

a=7 cm

b=12 cm

Right_triangle_with_labeled_sides

What is the area of the triangle?

Possible Answers:

square centimeters

$\sqrt{193}$ square centimeters

square centimeters

linear centimeters

Correct answer:

square centimeters

Explanation:

The formula for the area of a triangle is

$\frac{1}{2}bh$

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

$\frac{1}{2}(7)(12)=42$

or, based on the units given, 42 square centimeters

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

An equilateral triangle has a side of $4\; in$ .

What is the area of the triangle?

Possible Answers:

$8\; in^{2}$

$2\sqrt{3}\; in^{2}$

$2\sqrt{2}\; in^{2}$

$4\sqrt{3}\; in^{2}$

$6\; in^{2}$

Correct answer:

$4\sqrt{3}\; in^{2}$

Explanation:

An equilateral triangle has three congruent sides. The area of a triangle is given by $A = \frac{1}{2}bh$ where is the base and is the height.

The equilateral triangle can be broken into two 30-60-90 right triangles, where the legs are and and the hypotenuses is .

Using the Pythagorean Theorem we get $4^{2}=2^{2} + x^{2}$ or $x=2\sqrt{3}$ and the area is $A = \frac{1}{2}bh= \frac{1}{2}(4)(2\sqrt{3}) = 4\sqrt{3}$

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Example Question #9 : How To Find The Area Of A Right Triangle

The hypotenuse of a $30^{\circ }-60^{\circ }-90^{\circ }$ triangle measures eight inches. What is the area of this triangle (radical form, if applicable)?

Possible Answers:

$16 \; \textrm{in}^{2}$

It is impossible to tell from the information given.

$8\sqrt{3} \; \textrm{in}^{2}$

$8\sqrt{2} \; \textrm{in}^{2}$

$8\; \textrm{{in}}^{2}$

Correct answer:

$8\sqrt{3} \; \textrm{in}^{2}$

Explanation:

In a $30^{\circ }-60^{\circ }-90^{\circ }$ , the shorter leg is half as long as the hypotenuse, and the longer leg is $\sqrt{3}$ times the length of the shorter. Since the hypotenuse is 8, the shorter leg is 4, and the longer leg is $4\sqrt{3}$ , making the area:

$A = \frac{1}{2} bh = \frac{1}{2} \cdot 4 \cdot 4\sqrt{3} = 8\sqrt{3}$

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Example Question #7 : How To Find The Area Of A Right Triangle

$What\;is\;the\;area\;of\;\Delta GHJ?$

Possible Answers:

Correct answer:

Explanation:

$Area \;\Delta= \frac{1}{2}(base)(height)$

$\Delta GHF=\frac{1}{2}(5)(12)=\frac{1}{2}(60)=30$

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

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

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

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

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

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

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

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

Example Question #7 : How To Find The Area Of A Right Triangle

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

Example Question #9 : How To Find The Area Of A Right Triangle

Example Question #7 : How To Find The Area Of A Right Triangle

All Basic Geometry Resources

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