A triangle and a parallelogram have the same base and the same area if the side's of the triangle are 26 CM , 28 CM, AND 30CM , and thi. parallelograms stands on the base 28 CM , find the height of the parallelogram.
Answers
answer.
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.
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.
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.