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 cm2
Area of parallelogram ABCD = Area of ΔABE (given)
Base × Height = 336 cm2
28 cm × Height = 336 cm2
On rearranging, we get
Height = 336/28 cm = 12 cm
Thus, height of the parallelogram is 12 cm.
☛ Check: NCERT Solutions for Class 9 Maths Chapter 12
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.
☛ Related Questions:
- 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?
- An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (See Fig. 12.16), each piece measuring 20 cm, 50 cm, and 50 cm. How much cloth of each colour is required for the umbrella?
- A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in Fig. 12.17 How much paper of each shade has been used in it?
- A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm, and 35 cm (see Fig. 12.18). Find the cost of polishing the tiles at the rate of 50p per cm2.