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.