Area of Quadrilateral using Heron's formula

Chapter 10 Class 9 Herons Formula
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### Transcript

Question 9 A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field. Area of trapezium = 1/2 Sum of parallel sides Height = 1/2 (AB + DC) BF To calculate BF, we do the following steps Step 1: Draw BE AD Note AB DE Since, opposite sides are parallel, ABED is a parallelogram In parallelogram, opposite sides are equal BE = AD = 13 m & ED = AB = 10 m Also, EC = DC ED = 25 10 = 15 m Finding Area BEC by Herons formula Area BEC 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 = 14 m , b = 15m, c = 13 m s = ( + + )/2 Area of BEC = ( ( )( )( )) Putting a = 14 m , b = 15m, c = 13 m & s = 21 m = (21(21 13)(21 14)(21 15))m2 = (21(8)(7)(6)) = ((7 3) (8) (7) (2 3)) = ((7 7) (8 2) (3 3)) = ((7 7) (16) (3 3)) = ((72) (42) (32)) = ((7)2) ((4)2) ((3)2) = 7 4 3 = 84 m2 Since BEC has height BF and base EC, we use base height formula to find area Area of BEC = 1/2 Base Height Area of BEC = 1/2 CE BF 84 m2 = 1/2 15 m BF BF = 84 (2/15) m BF = 11.2 m Area of trapezium = 1/2 Sum of parallel sides Height = 1/2 (AB + DC) BF = 1/2 (10 + 25) 11.2 = 1/2 (35) 11.2 = 196 m2

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.