Question

pls find the area of this quadrilateral

Answer 1

Answer:138sq.cm

Step-by-step explanation:

divide triangle into 2 parts by diagonal.....find area of ABD and BCD by hero's formula as follows  :

Triangle BCD is a triangle with side lengths 9,12, and 15. Since 9, 12, and 15 are 3 times 3, 4, and 5, respectively, BCD is a right triangle with legs 9 and 12 and hypotenuse 15 so that its area is 1/2 (9)(12) = 54.  

Triangle ABD is a triangle with side lengths 13, 14, and 15. We can obtain its area in several ways. The most easiest way is to use Heron's formula for the area of a triangle which is given by  

A = [s(s - a)(s - b)(s - c)]^1/2, where a,b,and c are the side lengths and s = (a + b + c)/2 is the semi perimeter. Evaluating, we obtain s = (13 + 14 + 15)/2 = 21, so that  

A = [21(8)(7)(6)]^1/2 = 84.  

Thus the area of the quadrilateral is 54 + 84 = 138sq.cm.  

iS THIS detailed enough?^-^