Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

Question

Philoid · Accepted Answer

AB = 3cm, BC = 4cm, CD = 4cm, DA =5cm and AC = 5cm

Now, in

Using Pythagoras theorem,

AC² = BC² + AB²

5² = 3² + 4²

25= 16 + 9

25 = 25

Thus,

Triangle is right angled at B.

²

Now,

Perimeter of triangle(ACD) = 5 + 5 + 4

Semi perimeter of triangle (ACD) =

=

= 7cm

Using Heron’s formula,

Area of =

=

= cm²

= 9.17 cm² (approx.)

Area of quadrilateral ABCD = Area of

= 6 + 9.17

= 15.17 cm²