NCERT Class 9 Solutions: Heron's Formula (Chapter 12) Exercise 12.2 Part 3

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Area formula of rectangle,parallelogram and triangle

Area Formula of Rectangle,Parallelogram and Triangle

Area formula of rectangle,parallelogram and triangle

Q-4 A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are , and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

Solution:

Triangle and Parallelogram

Triangle and parallelogram. Side of the triangle are 26cm, 28cm and 30cm. Parallelogram base is on 28cm side.

Let’s find the area of the triangle, and then use the fact that triangle and base have same are to find the height of the parallelogram.

The sides of triangle are

Therefore, semi perimeter =

Using Heron’s formula, its area is

Given that,

Therefore, height of the parallelogram is

Q-5 A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?

Solution:

Rhombus PQRS With Given Dimensions

Rhombus PQRS, also two congruent triangles of equal area formed by its diagonals

Note that, diagonal PR divides the rhombus PQRS into two congruent triangles of equal areas. We find the area of rhombus by finding areas of each of the triangles.

Semi perimeter of =

Using heron's formula, area of the

Since the two triangles are congruent area of field =

Finally there are 18 cows, therefore area of grass field for each cow =