## Example Questions

### Example Question #1 : How To Find The Length Of The Side Of A Parallelogram In parallelogram  and . Find .   There is insufficient information to solve the problem.  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 . There is insufficient information to solve the problem.    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 . There is insufficient information to solve the problem.    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 .

There is insufficient information to solve the problem.     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 .      Explanation:

The formula for the area of a parallelogram is: By plugging in the given values, we get:  ### Example Question #1 : How To Find The Length Of The Side Of A Parallelogram  is a parallelogram with an area of . Find . There is insufficient information to solve the problem.    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.   ### All ACT Math Resources 