Question

ABCD is a quadrilateral field ABC equal to 40 metre BC is equal to 15 CD is equal to 28 metre is equal to 9 and angle Dab is equal to 90 degree find the area of the field​

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