The correct option is B 6+2√21 cm2
Quadrilateral ABCD can be divided into two triangles ABC and ADC.
The area of a triangle with sides a, b and c can be calculated using Heron's formula, given by:
Area =√s(s−a)(s−b)(s−c),
where 's' is the semi-perimeter.
[s=a+b+c2]
For △ABC,semi-perimeter =3+4+52=6 cm
Then, ar(△ABC)=√6×(6−3)×(6−4)×(6−5)=6 cm2
Similarly, for △ADC,
semi-perimeter=5+5+42=7 cm
ar(ADC)=√7×(7−5)×(7−5)×(7−4)=2√21 cm2
So, area of quadrilateral ABCD
= ar(ABC) + ar(ADC)
= 6+2√21 cm2