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Intermediate Geometry : How to find the length of the side of a parallelogram

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Example Question #1 : How To Find The Length Of The Side Of A Parallelogram

Find the perimeter of the following box in inches:

Geo_box

Possible Answers:

x + y + 19

xy + 7x + 12y +84

2x + 2y + 38

84xy

12x +7y

Correct answer:

2x + 2y + 38

Explanation:

The answer is 2x + 2y + 38 .

You can find the perimeter by adding all of its respective sides as such:

(12 + x) + (12 + x) + (7 + y) + (7 + y) .

Adding like terms will result in

2x + 2y + 38

If you chose xy + 7x + 12y +84 , you multiplied the two sides to find the area.

If you chose x + y + 19 , you only added two sides. Perimeter involves all 4 sides; so double the width and length.

Just remember, the width is 12 added to . Not 12 times the side of .

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Example Question #1 : How To Find The Length Of The Side Of A Parallelogram

A parallelogram has an area of $54\:cm^2$ . If the height is $6\:cm$ , what is the length of the base?

Possible Answers:

$9\:cm$

$4.5\:cm$

Cannot be determined

$12\:cm$

$18\:cm$

Correct answer:

$9\:cm$

Explanation:

If the area of a parallelogram is given as $54\:cm^2$ with a height of $6\:cm$ , we can refer back to the equation for the area of a parallelogram:

$A= b \cdot h$ , where is height and is the length of the base.

This very quickly becomes a problem of substituting in values and finding the value of an unknown variable, in this case, :

$54\:cm^2=6\:cm \cdot b$

$\frac{54\:cm^2}{6\:cm}=b$

$b=9\:cm$

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Example Question #1 : How To Find The Length Of The Side Of A Parallelogram

A parallelogram has a base of 10in and an area of 35in^2 . What is the height of the parallelogram?

Possible Answers:

1.25in

3in

3.25in

3.5in

Correct answer:

3.5in

Explanation:

In order to find the height of this parallelogram apply the formula: $A=base\times height$

$35=10\times height$

$height= \frac{35}{10}=3.5$

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Example Question #4 : How To Find The Length Of The Side Of A Parallelogram

A parallelogram has a height of 12ft and an area of 168ft^2 . What is the length of the base of the parallelogram?

Possible Answers:

15ft

14ft

12ft

10ft

Correct answer:

14ft

Explanation:

To find the missing side of this parallelgram apply the formula: $A=base\times height$

Thus, the solution is:

$168=12\times base$

$base=\frac{168}{12}=14$

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Example Question #2 : How To Find The Length Of The Side Of A Parallelogram

Given that a parallelogram has a height of 2.5ft and an area of 20ft^2 . Find the base of the parallelogram.

Possible Answers:

12ft

7.5ft

6.5ft

8ft

Correct answer:

8ft

Explanation:

In order to find the base of this parallelogram apply the formula: $Area=base\times height$

Thus, the solution is:

$20=base\times2.5$

$base=\frac{20}{2.5}$

base=8

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Example Question #2 : How To Find The Length Of The Side Of A Parallelogram

Given: Quadrilateral ABCD with diagonal $\overline{AC}$ ; $\bigtriangleup ABC \cong \bigtriangleup CDA$ .

True or false: From the information given, it follows that Quadrilateral ABCD is a parallelogram.

Possible Answers:

False

True

Correct answer:

True

Explanation:

Corresponding parts of congruent triangles are, by definition, congruent. Thus, from the statement $\bigtriangleup ABC \cong \bigtriangleup CDA$ , it follows that:

$\overline{AB} \cong \overline{CD}$ and $\overline{BC} \cong \overline{DA}$

Quadrilateral ABCD therefore has two sets of congruent opposite sides. This is a sufficient condition for the quadrilateral to be a parallelogram.

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Example Question #3 : How To Find The Length Of The Side Of A Parallelogram

Quadrilateral ABCD is both a rhombus and a rectangle.

True or false: Quadrilateral ABCD must be a square.

Possible Answers:

False

True

Correct answer:

True

Explanation:

A rhombus is defined to be a parallelogram with four congruent sides; a rectangle is defined to be a parallelogram with four right angles.

A square is defined to be a parallelogram with four congruent sides and four right angles. If a parallelogram is both a rhombus and a rectangle, then it fits both characteristics and is therefore a square.

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Intermediate Geometry : How to find the length of the side of a parallelogram

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : How To Find The Length Of The Side Of A Parallelogram

Example Question #1 : How To Find The Length Of The Side Of A Parallelogram

Example Question #1 : How To Find The Length Of The Side Of A Parallelogram

Example Question #4 : How To Find The Length Of The Side Of A Parallelogram

Example Question #2 : How To Find The Length Of The Side Of A Parallelogram

Example Question #2 : How To Find The Length Of The Side Of A Parallelogram

Example Question #3 : How To Find The Length Of The Side Of A Parallelogram

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