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Pre-Algebra : Geometry

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Example Questions

Example Question #61 : Geometry

Find the area of a parallelogram if the base length is $\displaystyle 2$ and the height is $\displaystyle 25$.

Possible Answers:

100 $\displaystyle 100$

$\displaystyle 50$

$\displaystyle 25$

$\displaystyle 75$

12.5 $\displaystyle 12.5$

Correct answer:

$\displaystyle 50$

Explanation:

Write the formula for thearea of a parallelogram.

A=bh $\displaystyle A=bh$

Substitute the dimensions.

$\displaystyle A=bh = 2(25)=50$

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Example Question #62 : Geometry

Find the area of a parallelogram with a base of 4 and a height of 40.

Possible Answers:

200 $\displaystyle 200$

160 $\displaystyle 160$

320 $\displaystyle 320$

$\displaystyle 80$

$\displaystyle 88$

Correct answer:

160 $\displaystyle 160$

Explanation:

Write the formula to find the area of a parallelogram.

A=bh $\displaystyle A=bh$

Substitute the dimensions.

$\displaystyle A=(4)(40)=160$

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Example Question #63 : Geometry

Find the area of a parallelogram if both the base and height have a length of 10.

Possible Answers:

$\displaystyle 50$

200 $\displaystyle 200$

$\displaystyle 20$

100 $\displaystyle 100$

$\displaystyle 10$

Correct answer:

100 $\displaystyle 100$

Explanation:

Write the area of the parallelogram.

A=bh $\displaystyle A=bh$

Substitute the dimensions.

$\displaystyle A=(10)(10)=100$

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Example Question #64 : Geometry

Find the area of a parallelogram if the base is 3 inches and the height is 8 inches.

Possible Answers:

$24 \textup{ inches} ^2$ $\displaystyle 24 \textup{ inches} ^2$

$12 \textup{ inches} ^2$ $\displaystyle 12 \textup{ inches} ^2$

$6 \textup{ inches} ^2$ $\displaystyle 6 \textup{ inches} ^2$

$576\textup{ inches}^2$ $\displaystyle 576\textup{ inches}^2$

$24 \textup{ inches}$ $\displaystyle 24 \textup{ inches}$

Correct answer:

$24 \textup{ inches} ^2$ $\displaystyle 24 \textup{ inches} ^2$

Explanation:

Write the formula for the area of a parallelogram.

A=bh $\displaystyle A=bh$

Substitute the dimensions.

$A= (3 \textup{ inches})(8\textup{ inches}) = 24 \textup{ inches} ^2$ $\displaystyle A= (3 \textup{ inches})(8\textup{ inches}) = 24 \textup{ inches} ^2$

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Example Question #16 : Area Of A Parallelogram

Find the area of a parallelogram if the base and height are x+1 $\displaystyle x+1$ and x^2 $\displaystyle x^2$, respectively.

Possible Answers:

x^3+x^2 $\displaystyle x^3+x^2$

$\displaystyle x^3+2x^2$

3x^2 $\displaystyle 3x^2$

$\displaystyle 2x^3+2x^2$

2x^2+x $\displaystyle 2x^2+x$

Correct answer:

x^3+x^2 $\displaystyle x^3+x^2$

Explanation:

Write the formula for the area of a parallelogram.

A=bh $\displaystyle A=bh$

Substitute the dimensions. Use the distributive property. The distibutive property means to multiply the monomial term, x^2 $\displaystyle x^2$, to each term within the parentheses. Remember when like bases are multiplied, their exponents are added together. Thus resulting in the following area.

$\displaystyle A=(x+1)(x^2) = x^3+x^2$

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Example Question #66 : Area

Find the area of a parallelogram with a base of $\displaystyle a$ and a height of a+1 $\displaystyle a+1$.

Possible Answers:

$\displaystyle 3a$

a^2+2 $\displaystyle a^2+2$

a^2+1 $\displaystyle a^2+1$

2a+2 $\displaystyle 2a+2$

a^2+a $\displaystyle a^2+a$

Correct answer:

a^2+a $\displaystyle a^2+a$

Explanation:

Write the formula to find the area of a parallelogram.

A=bh $\displaystyle A=bh$

Substitute the dimensions. Use the distributive property.

$\displaystyle A=a(a+1) = a^2+a$

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Example Question #67 : Area

Find the area of a parallelogram in $\textup{inches}$ $\displaystyle \textup{inches}$ if the base is $\textup{3 feet}$ $\displaystyle \textup{3 feet}$ and the height is $\textup{3 inches}$ $\displaystyle \textup{3 inches}$.

Possible Answers:

542 $\displaystyle 542$

108 $\displaystyle 108$

1296 $\displaystyle 1296$

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

$\displaystyle 9$

Correct answer:

108 $\displaystyle 108$

Explanation:

Convert the base from feet to inches. There are $\textup{12 inches}$ $\displaystyle \textup{12 inches}$ in a foot. Multiply the base by $\displaystyle 12$.

$b=3 \textup{ feet }\times \frac{12\textup{ inches }}{1 \textup{ foot}} = 36 \textup{ inches}$ $\displaystyle b=3 \textup{ feet }\times \frac{12\textup{ inches }}{1 \textup{ foot}} = 36 \textup{ inches}$

Write the area for a parallelogram.

A=bh $\displaystyle A=bh$

Substitute the new base and the height.

$\displaystyle A=(36)(3)=108$

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Example Question #65 : Geometry

Determine the area of a parallelogram with a base and height of $3\sqrt{5}$ $\displaystyle 3\sqrt{5}$.

Possible Answers:

225 $\displaystyle 225$

$\displaystyle 45$

$\displaystyle 50$

$\displaystyle 15$

$\displaystyle 75$

Correct answer:

$\displaystyle 45$

Explanation:

Write the formula to find the area of a parallelogram. Substitute the dimensions.

$A=bh = (3\sqrt5)(3\sqrt5) = 3\times 3\times 5 = 45$ $\displaystyle A=bh = (3\sqrt5)(3\sqrt5) = 3\times 3\times 5 = 45$

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Example Question #69 : Area

Find the area of a parallelogram with the base of $\frac{8}{3}$ $\displaystyle \frac{8}{3}$ and a height of $\frac{2}{7}$ $\displaystyle \frac{2}{7}$.

Possible Answers:

$\frac{32}{441}$ $\displaystyle \frac{32}{441}$

$\frac{16}{441}$ $\displaystyle \frac{16}{441}$

$\frac{10}{21}$ $\displaystyle \frac{10}{21}$

$\frac{62}{21}$ $\displaystyle \frac{62}{21}$

$\frac{16}{21}$ $\displaystyle \frac{16}{21}$

Correct answer:

$\frac{16}{21}$ $\displaystyle \frac{16}{21}$

Explanation:

Write the formula for the area of a parallelogram.

A=bh $\displaystyle A=bh$

Substitute the dimensions.

$A=\frac{8}{3} \times \frac{2}{7} = \frac{16}{21}$ $\displaystyle A=\frac{8}{3} \times \frac{2}{7} = \frac{16}{21}$

Remember, when multiplying fractions, multiply the numerators together and multiply the denominators together.

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Example Question #69 : Geometry

Find the area of a parallelogram in feet with a base of 11 inches and a height of 2 feet.

Possible Answers:

$\frac{11}{6} \textup{ feet}^2$ $\displaystyle \frac{11}{6} \textup{ feet}^2$

$22 \textup{ feet}^2$ $\displaystyle 22 \textup{ feet}^2$

$\frac{11}{6} \textup{ feet}$ $\displaystyle \frac{11}{6} \textup{ feet}$

$264 \textup{ feet}^2$ $\displaystyle 264 \textup{ feet}^2$

$264 \textup{ feet}$ $\displaystyle 264 \textup{ feet}$

Correct answer:

$\frac{11}{6} \textup{ feet}^2$ $\displaystyle \frac{11}{6} \textup{ feet}^2$

Explanation:

Convert the base dimension to feet. There are 12 inches in a foot.

$b= 11 \textup{ inches} \left(\frac{1\textup{ foot}}{12 \textup{ inches}}\right) = \frac{11}{12} \textup{ foot}$ $\displaystyle b= 11 \textup{ inches} \left(\frac{1\textup{ foot}}{12 \textup{ inches}}\right) = \frac{11}{12} \textup{ foot}$

Write the formula for the area of a parallelogram.

A=bh $\displaystyle A=bh$

Substitute the dimensions.

$A=\left(\frac{11}{12} \textup{ foot}\right)(2 \textup{ feet}) = \frac{11}{6} \textup{ feet}^2$ $\displaystyle A=\left(\frac{11}{12} \textup{ foot}\right)(2 \textup{ feet}) = \frac{11}{6} \textup{ feet}^2$

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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #61 : Geometry

Example Question #62 : Geometry

Example Question #63 : Geometry

Example Question #64 : Geometry

Example Question #16 : Area Of A Parallelogram

Example Question #66 : Area

Example Question #67 : Area

Example Question #65 : Geometry

Example Question #69 : Area

Example Question #69 : Geometry

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