# 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.

**Solution:**

Given: Area of the parallelogram = Area of the triangle

By using the area of the parallelogram formula, we can calculate the height of the parallelogram

By using Heron’s formula, we can calculate the area of a triangle.

Heron's formula for the area of a triangle is: Area = √s(s - a)(s - b)(s - c)

Where a, b, and c are the sides of the triangle, and s = Semi-perimeter = Half the Perimeter of the triangle

Let ABCD is a parallelogram and ABE is a triangle having a common base with parallelogram ABCD.

For ∆ABE, a = 30 cm, b = 26 cm, c = 28 cm

Semi Perimeter: (s) = Perimeter/2

s = (a + b + c)/2

= (30 + 26 + 28)/2

= 84/2

= 42 cm

By using Heron’s formula,

Area of a ΔABE = √s(s - a)(s - b)(s - c)

= √42(42 - 30)(42 - 28)(42 - 26)

= √42 × 12 × 14 × 16

= 336 cm^{2}

Area of parallelogram ABCD = Area of ΔABE (given)

Base × Height = 336 cm^{2}

28 cm × Height = 336 cm^{2}

On rearranging, we get

Height = 336/28 cm = 12 cm

Thus, height of the parallelogram is 12 cm.

**Video Solution:**

## 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.

### Class 9 Maths NCERT Solutions - Chapter 12 Exercise 12.2 Question 4:

**Summary:**

It is given that 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, we have found that the height of the parallelogram is 12 cm.