Parallelogram Area

Consider the following parallelogram.

a. Calculate the value of x. And then, calculate the length of AB.
b. Calculate the area of the parallelogram.

Quoted from : Exercise No 3, page 305
(Marsigit. 2009. Mathematics I for Junior High School. Jakarta: Yudhistira.)

Solution:
a. Base on the properties of parallelogram, the opposite sides are equal and parallel to each other. So, we can calculate the value of x.
                    AB = CD
              4x - 15 = 2x + 3
              4x - 2x = 3 + 15
                     2x = 18
                       x = 9

After we calculate the value of x, we can determine the length of AB.

                     AB = 4x - 15
                     AB = 4.9 - 15
                     AB = 36 - 15
                     AB =  21

Hence, the value of x is 9 cm and the length of AB is 21 cm.


b. The base of parallelogram ABCD is AB = 21 cm.
The height of parallelogram ABCD is DE = 10 cm.
Therefore, we can calculate the area as:

                       L = base x height
                       L = AB x DE
                       L = 21 x 10
                       L = 210

Hence, the area of parallelogram ABCD is 210 cm²