# ACT Math : Parallelograms

## Example Questions

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

Note: Figure NOT drawn to scale.

Give the perimeter of Parallelogram  in the above diagram.

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

Note: Figure NOT drawn to scale.

Give the perimeter of Parallelogram  in the above diagram.

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

Note: Figure NOT drawn to scale.

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

Explanation:

The perimeter of the parallelogram is

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

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

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

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

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

Note: Figure NOT drawn to scale.

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

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?

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

is a parallelogram. Find the length of diagonal .

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

is a parallelogram. Find the length of diagonal .

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

is a parallelogram. Find the length of diagonal .