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Pre-Algebra : Area of a Triangle

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Example Questions

Example Question #81 : Geometry

Given the following measurements of a triangle: base (b) and height (h), find the area.

$\small b = 4cm , h = 10cm$

Possible Answers:

$\small 20cm^{2}$

$\small 21cm^{3}$

3mm^3

$\small 18cm^{3}$

10m^2

Correct answer:

$\small 20cm^{2}$

Explanation:

The area of triangle is found using the formula

$\small A= \frac{1}{2}bh$ .

Provided with the base and the height, all we need to do is plug in the values and solve for A.

$\small A = \frac{1}{2}(4)(10) = 20cm^{2}$ .

Since this is asking for the area of a shape, the units are squared.

Thus, our final answer is $\small 20cm^{2}$ .

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Example Question #82 : Area

Given the following measurements of a triangle: base (b) and height (h), find the area.

$\small b = 10cm, h = 30cm$

Possible Answers:

205cm^2

$\small 55cm^{3}$

$\small 150cm^{2}$

$\small 50cm^{2}$

$\small 155cm^{2}$

Correct answer:

$\small 150cm^{2}$

Explanation:

The area of triangle is found using the formula

$\small A= \frac{1}{2}bh$ .

Provided with the base and the height, all we need to do is plug in the values and solve for A.

$\small \small A = \frac{1}{2}(10)(30) = 150cm^{2}$ .

Since this is asking for the area of a shape, the units are squared.

Thus, our final answer is $\small 150cm^{2}$ .

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Example Question #83 : Area

Given the following measurements of a triangle: base (b) and height (h), find the area.

$\small b = 13cm, h = 16cm$

Possible Answers:

$\small 184cm^{3}$

$\small 180cm^{3}$

110m^2

$\small 200cm^{3}$

$\small 104cm^{2}$

Correct answer:

$\small 104cm^{2}$

Explanation:

The area of triangle is found using the formula

$\small A= \frac{1}{2}bh$ .

Provided with the base and the height, all we need to do is plug in the values and solve for A.

$\small \small A = \frac{1}{2}(13)(16) = 104$ .

Since this is asking for the area of a shape, the units are squared.

Thus, our final answer is $\small \small 104cm^{2}$ .

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Example Question #11 : Area Of A Triangle

What is the area of an isoceles triangle that has a base length of 18 inches, side lengths of 15 inches and a vertical height of 12 inches?

Possible Answers:

$90\ \textup{in}^2$

$108\ \textup{in}^2$

$108\ \textup{in}^3$

$42\ \textup{in}^2$

$90\ \textup{in}^3$

Correct answer:

$108\ \textup{in}^2$

Explanation:

Area of a triangle is:- $\frac{1}{2}* \textup{base} * \textup{vertical height}$

Area is in Square Units.

$\frac{1}{2} * 18 *12 =$

9* 12 =

$108\ \textup{in}^2$

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Example Question #12 : Area Of A Triangle

The base of the triangle is . The height of the triangle is x+ 4 . What is the area of the triangle?

Possible Answers:

4x+4

2x+8

4x+16

2x+4

4x+8

Correct answer:

2x+8

Explanation:

Write the area for a triangle.

$A=\frac{1}{2}\times B\times H$

Substitute the base and height.

$A=\frac{1}{2}\times 4\times (x+4) = 2(x+4) = 2x+8$

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Example Question #12 : Area Of A Triangle

Find the area of a triangle with a base of and a height of .

Possible Answers:

5.5

$\frac{55}{2}$

Correct answer:

$\frac{55}{2}$

Explanation:

Write the formula for the area of a triangle.

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

Substitute the base and height.

$A=\frac{5\times11}{2} = \frac{55}{2}$

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Example Question #11 : Area Of A Triangle

What is the area of a right triangle if the hypotenuse is five, and a base leg is four?

Possible Answers:

Correct answer:

Explanation:

Write the area for a right triangle.

$A=\frac{1}{2}bh$

The height is unknown. In order to solve for the height, use the Pythagorean Theorem to find the unknown length.

a^2+b^2=c^2

4^2+b^2=5^2

b^2=5^2-4^2

b^2= 25-16

b^2 = 9

b=3

The height of the triangle is three. Substitute both leg dimensions to find the area.

$A=\frac{1}{2}(3\times 4) = 6$

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Example Question #14 : Area Of A Triangle

Find the area of an equilateral triangle with a perimeter of three.

Possible Answers:

$\frac{\sqrt3}{2}$

$\frac{\sqrt3}{6}$

$\frac{\sqrt6}{2}$

$\frac{\sqrt3}{4}$

$\frac{3\sqrt3}{2}$

Correct answer:

$\frac{\sqrt3}{4}$

Explanation:

Write the formula to find the area of an equilateral triangle given the side.

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

Since all three sides are equal in an equilateral triangle, divide the perimeter by three to obtain the length of one side. The side length is one.

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

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Example Question #15 : Area Of A Triangle

What is the area of a triangle if the base is and the height is x^2+2 ?

Possible Answers:

$\frac{x^2+x}{2}$

x^3+x

$\frac{x^3}{2}+x$

$\frac{x^3+x}{2}$

x^3+2x

Correct answer:

$\frac{x^3}{2}+x$

Explanation:

Write the formula to find the area of a triangle.

$A=\frac{1}{2} bh$

Substitute the base and height. Simplify the expression.

$A=\frac{1}{2} (x)(x^2+2) = \frac{1}{2} (x^3+2x) = \frac{x^3}{2}+x$

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Example Question #12 : Area Of A Triangle

Find the area of a triangle if the base is x^3 and the height is x^3+1 .

Possible Answers:

$\frac{x^9}{2}+x^3$

$\frac{x^6+x^3}{2}$

x^9+x^3

$\frac{x^9+x^3}{2}$

x^6+x^3

Correct answer:

$\frac{x^6+x^3}{2}$

Explanation:

Write the formula to find the area of a triangle.

$A=\frac{1}{2}bh$

Substitute the base and height.

From here multiply the monomial term, x^3 to each term within the parentheses. Also, recall the rules of exponents. When like bases are multiplied together their exponents are added.

$A=\frac{1}{2}(x^3)(x^3+1) = \frac{1}{2}(x^6+x^3) = \frac{x^6+x^3}{2}$

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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 #81 : Geometry

Example Question #82 : Area

Example Question #83 : Area

Example Question #11 : Area Of A Triangle

Example Question #12 : Area Of A Triangle

Example Question #12 : Area Of A Triangle

Example Question #11 : Area Of A Triangle

Example Question #14 : Area Of A Triangle

Example Question #15 : Area Of A Triangle

Example Question #12 : Area Of A Triangle

All Pre-Algebra Resources

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