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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

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11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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 #16 : 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:

x^6+x^3

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

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

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

x^9+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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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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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

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 #16 : Area Of A Triangle

Example Question #21 : Area Of A Triangle

Example Question #22 : Area Of A Triangle

Example Question #23 : Area Of A Triangle

All Pre-Algebra Resources

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