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: 33cm and 12cm. What is the area of the parallelogram?

Answer 1

By definition, a parallelogram is merely a quadrilateral. Its key characteristics are having two sets of parallel sides. Consequently, it would have two sets of equal lengths, denoted as a and b. A perpendicular bisector is the red line in the picture that bisects length b into two lengths while creating a right angle. The area of a parallelogram is

A = bh, where
b is the side that meets with h
h is the perpendicular height of the parallelogram

Since h is not known, we have to solve it first through applying the pythagorean theorem.

h = √29^2 - 12^2 = 26.4 m

Thus,

A = (12 cm + 33 cm)(26.4 cm)
A = 1,188 square centimeters