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Pre-Algebra : Geometry

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Example Questions

Example Question #71 : Geometry

Find the area of the parallelogram if the base side is and the height is .

Possible Answers:

15x^2

$\frac{15}{2}x^2$

16x

30x^2

Correct answer:

15x^2

Explanation:

Write the area of the parallelogram.

A=bh

Substitute the dimensions.

A=(3x)(5x) = 15x^2

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Example Question #72 : Geometry

Find the area of a parallelogram if the base is 13 and the height is 9.

Possible Answers:

112

117

224

Correct answer:

117

Explanation:

Write the formula for the area of a parallelogram.

A=bh

Substitute the base and height into the equation.

A=(13)(9) = 117

When multiplying two integers first multiply the ones place from each integer:

$9\cdot 3=27$

The seven will stay in the ones place but the two will be carried over. Now multiply the one integer with the tens integer and add the carried over term to that:

(9) (1)+2=9+2=11

The eleven represents the hundreds and tens spot. To get the final answer combine the ones digit to the hundreds and tens digit:

110+7=117

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Example Question #23 : Area Of A Parallelogram

Find the area of a parallelogram with the base of 5x^3 and a height of 10x^2 .

Possible Answers:

30 x^6

50 x^5

15 x^5

50 x^6

15 x^6

Correct answer:

50 x^5

Explanation:

Write the area formula of a parallelogram.

A=bh

Substitute the dimensions.

A=(5x^3)(10x^2)

Separate out the terms for clarity.

$A=5\cdot x\cdot x\cdot x\cdot 10\cdot x \cdot x$

There are five which could be combined as x^5 . Multiply the integers as well.

The area is: 50 x^5

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Example Question #24 : Area Of A Parallelogram

Solve for the area of a parallelogram if the base is and the height is .

Possible Answers:

102

408

204

297

594

Correct answer:

297

Explanation:

Write the formula for the area of a parallelogram.

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

Substitute the base and the height into the equation.

A=3(99) = 297

The area of the parallelogram is 297 .

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Example Question #25 : Area Of A Parallelogram

If the parallelogram base is 5 inches and the height is 8 inches, what must be the area of the parallelogram in inches?

Possible Answers:

$20 \textup{ inches}^2$

$40 \textup{ inches}^2$

$40 \textup{ inches}$

$\frac{10}{3} \textup{ inches}^2$

$\frac{10}{3} \textup{ inches}$

Correct answer:

$40 \textup{ inches}^2$

Explanation:

Write the area formula for a parallelogram.

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

Substitute the dimensions into the formula.

$A= 5 \textup{ inches} \times 8 \textup{ inches} = 40 \textup{ inches}^2$

The area is always in units squared.

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Example Question #27 : Area Of A Parallelogram

Find the area of a parallelogram with a base edge of and a height of .

Possible Answers:

31.5

Correct answer:

Explanation:

Write the formula for the area of a parallelogram.

A=bh

Substitute the base and the height into the formula and multiply the dimensions.

A=(9)(7) = 63

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Example Question #28 : Area Of A Parallelogram

Find the area of a parallelogram with a base of 9cm and height that is half the base.

Possible Answers:

$81\text{cm}^2$

$40.5\text{cm}^2$

$40.5\text{cm}$

$36\text{cm}$

$36.5\text{cm}^2$

Correct answer:

$40.5\text{cm}^2$

Explanation:

The formula to find the area of a parallelogram is

$A=b \cdot h$

where b is the base and h is the height. We know the base is 9cm and the height is half of the base. Therefore, the height is 4.5cm. Substituting into the formula, we get

$A = 9\text{cm} \cdot 4.5\text{cm}$

$A = 40.5\text{cm}^2$

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Example Question #1 : Area Of A Triangle

Find the area of the triangle:
Problem_12

Possible Answers:

Correct answer:

Explanation:

The area of the triangle can be determined using the following equation:
$\small A=\frac{1}{2}bh$

The base is the side of the triangle that is intersected by the height.

$\small A=\frac{1}{2}(4)(12)=(2)(12)=24$

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Example Question #2 : Area Of A Triangle

The length of the base of a triangle is inches. The height of the triangle is inches. Find the area of the triangle.

Possible Answers:

$7.5\:in^{2}$

$50\:in^{2 }$

$15\:in^{2}$

$25\:in^{2}$

$30\:in^{2}$

Correct answer:

$25\:in^{2}$

Explanation:

The correct answer is $Area = 25 in^{2}$ .

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

To solve the equation, plug in the base and height: $\frac{1}{2} \cdot5\cdot10$

Once you multiply these three numbers, the answer you find is .

The units for area are always squared, so the unit is $in^{2}$ .

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Example Question #3 : Area Of A Triangle

If a right triangle has dimensions of inches by inches by inches, what is the area?

Possible Answers:

$8\textup{ in} ^2$

$4\textup{ in} ^2$

$6\textup{ in} ^2$

$12\textup{ in} ^2$

Correct answer:

$6\textup{ in} ^2$

Explanation:

The question is asking you to find the area of a right triangle.

First you must know the equation to find the area of a triangle,

$A=\frac{1}{2}( base \cdot height)$ .

A right triangle is special because the height and base are always the two smallest dimensions.

This makes the equation

$\frac{1}{2}( 3\cdot 4)=\frac{1}{2}\cdot 12=\frac{12}{2}=6$

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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #71 : Geometry

Example Question #72 : Geometry

Example Question #23 : Area Of A Parallelogram

Example Question #24 : Area Of A Parallelogram

Example Question #25 : Area Of A Parallelogram

Example Question #27 : Area Of A Parallelogram

Example Question #28 : Area Of A Parallelogram

Example Question #1 : Area Of A Triangle

Example Question #2 : Area Of A Triangle

Example Question #3 : Area Of A Triangle

All Pre-Algebra Resources

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