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ACT Math : 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

Parallelogram_2

In parallelogram ABCD , $\overline{AB} = 10$ and $\measuredangle A = 60^{\circ}$ . Find $\overline{CD}$ .

Possible Answers:

There is insufficient information to solve the problem.

$8\sqrt{3}$

Correct answer:

Explanation:

In a parallelogram, opposite sides are congruent. Thus,

$\overline{AB} = \overline{CD}$

$10 = \overline{CD}$

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

Parallelogram_2

In parallelogram ABCD , $\overline{BC} = 30$ and $\measuredangle B = 120^{\circ}$ . Find $\overline{AD}$ .

Possible Answers:

There is insufficient information to solve the problem.

Correct answer:

Explanation:

In a parallelogram, opposite sides are congruent.

$\overline{BC} = \overline{AD}$

$30 = \overline{AD}$

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

Parallelogram_9

Parallelogram ABCD has an area of 375 . If h = 15 , find $\overline{BC}$ .

Possible Answers:

There is insufficient information to solve the problem.

12.5

Correct answer:

Explanation:

The area of a parallelogram is given by:

A = bh

In this problem, the height is given as and the area is 375 . Both $\overline{AD}$ and $\overline{BC}$ are bases.

$375 = \left ( 15\right )\left ( \overline{BC} \right )$

$\overline{BC} = 25$

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

Parallelogram_10

ABCD is a parallelogram. Find $\overline{AB}$ .

Possible Answers:

There is insufficient information to solve the problem.

21.5

23.9

17.8

10.7

Correct answer:

23.9

Explanation:

$\overline{AB}$ is the hypotenuse of the right triangle formed when we draw the height of the parallelogram. Because it is a right triangle, we can use SOH CAH TOA to solve for $\overline{AB}$ . With respect to $\measuredangle A$ , we know the opposite side of the triangle and we are looking for the hypotenuse. Thus, we can use the sine function to solve for $\overline{AB}$ .

$\sin \left ( \theta\right ) = \frac{\textup{opposite}}{\textup{hypotenuse}}$

$\sin\left ( 42^{\circ}\right ) = \frac{16}{\overline{AB}}$

$\overline{AB} = \frac{16}{\sin\left ( 42^{\circ}\right )}$

$\overline{AB} = 23.9$

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

Find the length of the base of a parallelogram with a height of and an area of 204 .

Possible Answers:

144

Correct answer:

Explanation:

The formula for the area of a parallelogram is:

A = bh

By plugging in the given values, we get:

$204 = b\cdot12$

b = 17

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

Parallelogram_11

ABCD is a parallelogram with an area of 510 . Find $\overline{AB}$ .

Possible Answers:

There is insufficient information to solve the problem.

Correct answer:

Explanation:

In order to find $\overline{AB}$ , we must first find . The formula for the area of a parallelogram is:

A = bh

We are given 510 as the area and as the base.

$510 = 34\cdot h$

h = 15

Now, we can use trigonometry to solve for $\overline{AB}$ . With respect to $\measuredangle A$ , we know the opposite side of the right triangle and we are looking for the hypotenuse. Thus, we can use the sine function.

$\sin\left ( \theta\right ) = \frac{\textup{opposite}}{\textup{hypotenuse}}$

$\sin\left ( 62^{\circ}\right ) = \frac{15}{\overline{AB}}$

$\overline{AB} = \frac{15}{\sin \left ( 62^{\circ}\right )} = 17$

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ACT Math : How to find the length of the side of a parallelogram

Study concepts, example questions & explanations for ACT Math

All ACT Math 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 #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

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