### All ACT Math Resources

## 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:**

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:**

In a parallelogram, opposite sides are congruent.

### Example Question #3 : 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:**

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 #81 : Quadrilaterals

is a parallelogram. Find .

**Possible Answers:**

There is insufficient information to solve the problem.

**Correct answer:**

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 #5 : 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:**

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:**

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.

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