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

## Example Questions

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

In parallelogram  and . Find .

Possible Answers:

There is insufficient information to solve the problem.

Correct answer:

Explanation:

In a parallelogram, opposite sides are congruent. Thus,

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

In parallelogram  and . Find .

Possible Answers:

There is insufficient information to solve the problem.

Correct answer:

Explanation:

In a parallelogram, opposite sides are congruent.

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

Parallelogram  has an area of . If , find .

Possible Answers:

There is insufficient information to solve the problem.

Correct answer:

Explanation:

The area of a parallelogram is given by:

In this problem, the height is given as  and the area is . Both  and  are bases.

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

is a parallelogram. Find .

Possible Answers:

There is insufficient information to solve the problem.

Correct answer:

Explanation:

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 . With respect to , 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 .

### 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 .

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a parallelogram is:

By plugging in the given values, we get:

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

is a parallelogram with an area of . Find .

Possible Answers:

There is insufficient information to solve the problem.

Correct answer:

Explanation:

In order to find , we must first find . The formula for the area of a parallelogram is:

We are given  as the area and  as the base.

Now, we can use trigonometry to solve for . With respect to , we know the opposite side of the right triangle and we are looking for the hypotenuse. Thus, we can use the sine function.