web analytics

Ex 12.2, 4 - A triangle and a parallelogram have same base - Ex 12.2

  1. Chapter 12 Class 9 Herons Formula
  2. Serial order wise
Ask Download

Transcript

Ex 12.2, 4 A triangle and a parallelogram have the same base and the same area. If the sides of triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram. Given that Area of parallelogram = Area of triangle Base × Height = Area of triangle 28 × Height = Area of triangle Height = 1/28 × Area of triangle Finding Area of triangle Area of triangle Area of triangle = √(s(s−a)(s−b)(s −c)) Here, s is the semi-perimeter, and a, b, c are the sides of the triangle Here, a = 26 , b = 28 , c = 30 s = (𝑎 + 𝑏 + 𝑐)/2 Area of triangle = √(42(42 −26)(42 −28)(42 −30)) cm2 = √(42(16)(14)(12)) = √((14×3)×(16)×(14)×(12)) = √((14×14)× (12×3)×(16) ) = √((142)× (36)×(16) ) = √((142)× (62)×(42) ) = √((14)2) × √((6)2) × √((4)2) = 14 × 6 × 4 = 336 cm2 Thus, Area of triangle = 336 cm2 Now, Height = 1/28 × Area of triangle Height  = 1/28 × 336 Height  = 12 cm Therefore, the height of the parallelogram is 12 cm.

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
Jail