two adjacent sides of a parallelogram measure 15 cm and 20 cm while the diagonal opposite their common vertex measure 25 cm.find the area of he parallelogram.

To find the area of the parallelogram, we can use the formula:

Area = base × height

In a parallelogram, the base can be any of its sides, and the height is the perpendicular distance between the base and its opposite side.

Since we have two adjacent sides of lengths 15 cm and 20 cm, we can choose one of them as the base. Let's choose the side with length 15 cm as the base.

Now, we need to find the height. We are given that the diagonal opposite the common vertex measures 25 cm. In a parallelogram, the diagonals bisect each other. Therefore, the height of the parallelogram is half of the diagonal length. So, the height of our parallelogram is 25 cm / 2 = 12.5 cm.

Now, we can plug in the values into the formula:

Area = base × height = 15 cm × 12.5 cm = 187.5 cm²

Therefore, the area of the parallelogram is 187.5 square cm.

As 25^2=625 & 15^2+20^2=225+400=625 from Pythagoras theorem it's a right angle triangle therefore the parallelogram is a rectangle. So area= 15*20=300 cm^2