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Pre-Algebra : Area of a Triangle

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Example Questions

Example Question #21 : Area Of A Triangle

Find the area of a triangle in yards if the side lengths of the triangle are 36 inches, 3 feet, and 1 yard.

Possible Answers:

$\frac{2\sqrt{3}}{3}$

$\frac{3}{4}$

108

$\frac{1}{2}$

$\frac{\sqrt3}{4}$

Correct answer:

$\frac{\sqrt3}{4}$

Explanation:

First convert all the dimensions to yards. There are 3 feet in 1 yard, and 12 inches in 1 foot.

$36\textup{ inches} \left(\frac{1\textup{ foot}}{12\textup{ inches}}\right)\left(\frac{1\textup{ yard}}{3\textup{ feet}}\right) = 1 \textup{ yard}$

The side lengths of the triangle are 1 yard by 1 yard by 1 yard. We can then see that this is an equilateral triangle.

Write the formula for the area of an equilateral triangle.

$A=\frac{\sqrt3}{4}a^2$

Substitute the side.

$A=\frac{\sqrt3}{4}(1)^2 = \frac{\sqrt3}{4}$

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Example Question #22 : Area Of A Triangle

A right triangle has a base of 6 and a height of 10. What is the area of the triangle?

Possible Answers:

Correct answer:

Explanation:

Write the formula for the area of a triangle. The area is half the product of the base and the height.

$A=\frac{bh}{2}$

Substitute the base and height into the equation.

$A=\frac{(6)(10)}{2} =\frac{60}{2} = 30$

The area of the triangle is 30.

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Example Question #23 : Area Of A Triangle

Solve for the area of a right triangle if the hypotenuse is and the height is .

Possible Answers:

Correct answer:

Explanation:

Write the area formula for triangles.

$A=\frac{bh}{2}$

The base is unknown. To find this dimension, use the Pythagorean Theorem.

a^2+b^2 = c^2

Substitute the hypotenuse into and the height into . Solve for the base.

6^2+b^2 = 10^2

Isolate the variable b^2 by subtracting 6^2 on both sides of the equation.

b^2 = 10^2-6^2

Simplify the squares on the right side of the equation.

b^2 = 100-36

Subtract the left side.

b^2 = 64

Square root both sides of the equation to eliminate the square root.

$\sqrt{b^2} = \sqrt{64}$

We will only consider the positive root because length cannot be a negative value.

b=8

The base is 8. Substitute the base and height to find the area.

$A=\frac{(8)(6)}{2} = \frac{48}{2} =24$

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Example Question #24 : Area Of A Triangle

If the base of a triangle is and the height is , what is the area of the triangle?

Possible Answers:

12x

18x^2

4x^2

8x^2

6x^2

Correct answer:

4x^2

Explanation:

Write the formula for finding the area of a triangle.

$A=\frac{\textup{ Base} \times \textup{ Height}}{2}$

Substitute the base and the height.

$A=\frac{2x\times 4x}{2}$

Multiply the numerator.

$A=\frac{8x^2}{2}$

Divide by two.

The area is: A=4x^2

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Example Question #25 : Area Of A Triangle

Find the area with a base of and a height of 6x^2 .

Possible Answers:

8x^3

x+3x^2

4x+12x^2

12x^3

6x^3

Correct answer:

6x^3

Explanation:

Write the formula for the area of a triangle.

$A=\frac{bh}{2}$

Substitute the base and the height.

$A=\frac{(2x)(6x^2)}{2}$

Cancel out the two in the numerator and denominator.

$A=\frac{(2x)(6x^2)}{2} = x(6x^2)$

Multiply both terms together.

A=6x^3

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Example Question #13 : How To Find The Area Of A Triangle

What is the area (in square feet) of a triangle with a base of feet and a height of feet?

Possible Answers:

Correct answer:

Explanation:

The area of a triangle is found by multiplying the base times the height, divided by .

$Area =\frac{base\cdot height}{2}$

$Area =\frac{4\cdot 7}{2}$

Area=14

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Example Question #14 : How To Find The Area Of A Triangle

What is the area of a triangle with a base of and a height of ?

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a triangle is $\dpi{100} Area=\frac{1}{2}\times base\times height$ .

Plug the given values into the formula to solve:

$\dpi{100} Area=\frac{1}{2}\times 12\times 3$

$\dpi{100} Area=\frac{1}{2}\times 36$

$\dpi{100} Area=18$

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Example Question #26 : Area Of A Triangle

The base of a triangle is inches, and the height of the triangle is inches. What is the area of the triangle?

Possible Answers:

in^2

Correct answer:

in^2

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two.

The best answer is:

$A=\frac{b\times h}{2}=\frac{2\times 9}{2}=9$

in^2

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Example Question #27 : Area Of A Triangle

The base of a triangle is inches, and the height is inches. What is its area?

Possible Answers:

in^2

Correct answer:

in^2

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two.

The best answer is:

$A=\frac{b\times h}{2}=\frac{4\times 7}{2}=\frac{28}{2}=14$

in^2

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Example Question #28 : Area Of A Triangle

The base of a triangle is inches, and the height of the triangle is inches. What is the area of the triangle?

Possible Answers:

square inches

Correct answer:

square inches

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two. The best answer is:

square inches

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Pre-Algebra : Area of a Triangle

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #21 : Area Of A Triangle

Example Question #22 : Area Of A Triangle

Example Question #23 : Area Of A Triangle

Example Question #24 : Area Of A Triangle

Example Question #25 : Area Of A Triangle

Example Question #13 : How To Find The Area Of A Triangle

Example Question #14 : How To Find The Area Of A Triangle

Example Question #26 : Area Of A Triangle

Example Question #27 : Area Of A Triangle

Example Question #28 : Area Of A Triangle

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