Question

find area of a quadrilateral in which AB=7cm BE=6cm cd=12cm da=15cm and ac=9cm

Answer 1

Answer:

area of quadrilateral ABCD= Area of triangle ABC + Area of triangle ADC

Area of trianlge= sqrt(s(s-a)(s-b)(s-c))

FOR area of triangle ABC

s=(7+6+9)/2=11

area of triangle ABC=sqrt(11(11-7)(11-6)(11-9))

=sqrt(440)

= 20.9761

similarly,

area of triangle ADC=54

therefore area of quadrilateral ABCD=20.9761+ 54

=74.9761

Answer 2

ar(ABCD) = ar(ADC) + ar(ABC)

Now,
In ∆ADC,
s = 15+12+9/2 = 18cm
by Heron's Formula,
area = √s(s-a)(s-b)(s-c)
= √18(18-15)(18-12)(18-9)
= √3×3×2×3×3×2×3×3
= 3×2×3×3
= 54cm² _____(i)

In ∆ABC,
s = 7+6+9/2 = 11cm
by Heron's Formula,
area = √s(s-a)(s-b)(s-c)
= √11(11-7)(11-6)(11-9)
= √11×2×2×5×2
= 2√11×2×5
= 2√110
= 2 × 10.49
= 20.98cm² _____(ii)

Now,
Area of quadrilateral = (i) + (ii)
= 54 + 20.98
= 74.98cm²