Question

EXERCISE 12.2
1. Find the area of a quadrilateral ABCD is which AB = 3 cm, BC = 4 cm, CD = 4 cm,
DA = 5 cm and AC = 5 cm.
[NCERT]​

Answer 1

answer

In △ABC

semi-perimeter, S=

2

3+4+5

=

2

12

=6

ar(△ABC)=

6(6−3)(6−4)(6−5)

=

6×3×2×1

=

36

=6cm

2

In △ACD,

semi-perimeter, S=

2

5+5+4

=

2

14

=7

Applying Heron's formula :

S(S−a)(S−b)(S−c)

ar(△ACD)=

7(7−5)(7−5)(7−4)

=

7×2×2×3

=

84

=2

21

cm

2

∴ Area of quadrilateral ABCD=ar(△ABC)+ar(△ACD)=(6+2

21

)cm

2

solution

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