Q24 of 33 Page 12

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm, and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

To Find: Height of the parallelogram

Given: Sides of triangle are 26 cm, 28 cm, and 30 cm


Base of parallelogram = 28 cm


Concept Used:


If sides of a triangle are a, b, and c, then area of a triangle is given by:



Where s = semiperimeter of the triangle



Area of parallelogram = base × height


Explanation:


Area of triangle = Area of parallelogram


Let us find the area of triangle first.





s = 42 cm




Area = 144√7 cm2


Now,


Area of parallelogram = 28 × height


Therefore,


28 × height = 144√7




Hence, the height of the parallelogram is


More from this chapter

All 33 →
21

The lengths of the sides of triangle ABC are consecutive integers. If triangle ABC has the same perimeter as an equilateral triangle with a side of length 9 cm, what is the length of the shortest side of triangle ABC?

 22

A hand fan is made by stitching 10 equal size triangular strips of two different types of paper as shown in the figure. The dimensions of equal strips are 25 cm, 25 cm, and 14 cm. Find the area of each type of paper needed to make the hand fan.

 23

Radha made a picture of an airplane with colored paper as shown in Figure. Find the total area of the paper used.

 25

Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on the land and produce different crops to suffice the needs of their family. She divided the land into two equal parts. If the perimeter of the land is 400 m and one of the diagonals is 160 m, how much area each of them will get?