A triangle and a parallelogram have the same base and 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.
Answers
Answer:
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.
Firstly find the area of a triangle by heron's formula and area of parallelogram then equate their areas to calculate the height of a parallelogram.
Given:
Sides of the triangle are 26cm, 28cm , 30cm.
Base 28cm
Solution:
Let the Length of the sides of the triangle are a=26 cm, b=28 cm and c-30 cm.
Let s be the semi perimeter of the triangle.
s=(a+b+c)/2
s=(26+28+30)/2= 84/2= 42 cm
s = 42 cm
Using heron's formula,
Area of the triangle = √s (s-a) (s-b) (s-c)
= √42(42 - 26) (46-28) (46 - 30)
= √42 × 16 × 14 × 12
=√7×6×16×2×7×6×2
√7x7x6×6×16×2×2
7x6x4x2= 336 cm²
Let height of parallelogram be h.& Base= 28 (given)
Area of parallelogram = Area of triangle (given)
[Area of parallelogram -base x height]
28× h = 336
h = 336/28 cm
h = 12 cm
Hence,
The height of the parallelogram is 12 cm.