Q. 24.0( 351 Votes )

Find the area of

Answer :


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

To find: Area of quadrilateral ABCD.
Now we can divide the quadrilateral into two separate triangles and then calculate their area.
Now, in
 Δ ABC,

Using Pythagoras theorem,

AC2 = BC2 + AB2

52 = 32 + 42

25= 16 + 9

25 = 25

Thus,

Triangle is right angled triangle and since AB and BC are smaller sides so they work as legs.

And we know that,


Now,

Perimeter of Δ ACD = 5 + 5 + 4

Semi perimeter of Δ ACD =

=

= 7 cm

Using Heron’s formula,

Area of  =

where, s = semi perimeter of the triangle and a, b, and c are the sides of the triangle

=

=

= cm2

Take √21 = 4.58

= 9.16 cm2 (approx.)

Area of quadrilateral ABCD = Area of  Δ ABC+ Area of  Δ ACD

= 6 + 9.16

= 15.16 cm2

By rounding off,

= 15.2 cm2 ( approx)

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