Question

The length of the shorter side of a parallelogram is 29 cm. Perpendicular line segment, which goes through the point of intersection of the diagonals to the longer side divides this longer side into two segments: 33 cm and 12 cm. What is the area of the parallelogram?

Answer 1

A = 900$cm^{2}$

The area of a parallelogram can be found by taking its base (b) and multiplying by the height (h). The base has the measure of 33 +12 = 45 cm. Now, you just need to find the height of the parallelogram. The height can be found by using the pythagorean theorem ($a^{2} + b^{2} = c^{2}$. 

So, when simplified the height of the parallelogram will be found from $\sqrt{ 29^{2} - 21^{2}}$

The height is 20 cm. The base is 45 cm. 45 x 20 = 900.