Question

find the area of a quadrilateral ABCD in which ab is equal to 3 cm BC is equal to 4 cm is equal to 4 cm is equal to 5 cm and ac is equal to 5 cm​

Answer 1

For triangle ABC

AC2=BC2+AB2

25 = 9 + 16

So, triangle ABC is a right angle triangle right angled at point R

Area of triangle ABC = 12×AB×BC

= 12×3×4

= 6 cm2

From triangle CAD

Perimeter = 2s = AC + CD + DA

2s = 5 cm+ 4 cm+ 5 cm

2s   = 14 cm

s = 7 cm

By using Heron’s Formula

Area of the triangle CAD = s×(s−a)×(s−b)×(s−c)−−−−−−−−−−−−−−−−−−−−−−−−√

= 7×(7−5)×(7−4)×(7−5)−−−−−−−−−−−−−−−−−−−−−−−−√

= 9.16cm2

Area of ABCD = Area of ABC + Area of CAD

= (6+9.16) cm2

= 15.16cm2