ACT Math : Parallelograms

Study concepts, example questions & explanations for ACT Math

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Example Questions

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

Parallelogram2

Note: Figure NOT drawn to scale.

Give the perimeter of Parallelogram  in the above diagram.

Possible Answers:

Correct answer:

Explanation:

By the 30-60-90 Theorem, the length of the short leg of  is the length of the long leg divided by , so 

Its hypotenuse has twice the length of the short leg, so 

The perimeter of the parallelogram is

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

Parallelogram1

Note: Figure NOT drawn to scale.

Give the perimeter of Parallelogram  in the above diagram.

Possible Answers:

Correct answer:

Explanation:

By the 45-45-90 Theorem, the lengths of the legs of are equal, so

Its hypotenuse has measure  that of the common measure of its legs, so 

The perimeter of the parallelogram is

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

Parallelogram

Note: Figure NOT drawn to scale.

To the nearest tenth, give the perimeter of Parallelogram  in the above diagram.

Possible Answers:

Correct answer:

Explanation:

 

 

The perimeter of the parallelogram is

Example Question #5 : How To Find The Perimeter Of A Parallelogram

Parallelogram1

In the above figure, Parallelogram  has area 100. To the nearest tenth, what is its perimeter?

Possible Answers:

Correct answer:

Explanation:

By the 45-45-90 Theorem, . Since  and  are its base and height:

Also by the 45-45-90 Theorem,

The perimeter of the parallelogram is

Example Question #6 : How To Find The Perimeter Of A Parallelogram

Parallelogram2

In the above figure, Parallelogram  has area 100. To the nearest tenth, what is its perimeter?

Possible Answers:

Correct answer:

Explanation:

By the 30-60-90 Theorem, 

The area of the parallelogram is the product of height  and base , so 

Also by the 30-60-90 Theorem,

The perimeter of the parallelogram is

Example Question #7 : How To Find The Perimeter Of A Parallelogram

Parallelogram

Note: Figure NOT drawn to scale.

In the above figure, Parallelogram  has area 100. To the nearest tenth, what is its perimeter?

Possible Answers:

Correct answer:

Explanation:

The area of the parallelogram is the product of height  and base , so 

 

The perimeter of the parallelogram is

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

If a rectangular plot measures  by , what is the length of the diagonal of the plot, in feet?

Possible Answers:

Correct answer:

Explanation:

To answer this question, we must find the diagonal of a rectangle that is  by . Because a rectangle is made up of right angles, the diagonal of a rectangle creates a right triangle with two of the sides. 

Because a right triangle is formed by the diagonal, we can use the Pythagorean Theorem, which is:

 and  each represent a different leg of the triangle and  represents the length of the hypotenuse, which in this case is the same as the diagonal length. 

We can then plug in our known values and solve for 

We now must take the square root of each side so that we can solve for 

Therefore, the diagonal of the rectangle is .

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

Parallelogram_12

 is a parallelogram. Find the length of diagonal .

Possible Answers:

Correct answer:

Explanation:

To find the length of the diagonal, we can consider only the triangle  and use the law of cosines to find the length of the unknown side.

The Law of Cosines:

Where  is the length of the unknown side,  and  are the lengths of the known sides, and  is the angle between  and 

From the problem:

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

Parallelogram_13

 is a parallelogram. Find the length of diagonal .

Possible Answers:

Correct answer:

Explanation:

To find the length of the diagonal, we can consider only the triangle  and use the law of cosines to find the length of the unknown side.

The Law of Cosines:

Where  is the length of the unknown side,  and  are the lengths of the known sides, and  is the angle between  and 

From the problem:

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

Parallelogram_15

 is a parallelogram. Find the length of diagonal .

Possible Answers:

Correct answer:

Explanation:

To find the length of the diagonal, we can consider only the triangle  and use the law of cosines to find the length of the unknown side.

The Law of Cosines:

Where  is the length of the unknown side,  and  are the lengths of the known sides, and  is the angle between  and 

From the problem:

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