Question

in a quadrilateral ABCd, AB=28cm,BC=26cm,CD=50cm,DA=40cmand the diagonal AC=30cm.find the area of the quadrilateral.

Answer 1

further solution you should do on your own

Answer 2

Answer: 936 cm²

Step-by-step explanation:

Area of ABCD = ar Δ  ADC + ar Δ ABC

Now By herons formula

$s=\dfrac{a+b+c}{2} \\\\Area = \sqrt{s(s-a)(s-b)(s-c)}$

For  Δ  ADC a= 40 cm , b= 50 cm , c= 30 cm

$\therefore s= \dfrac{40+50+30}{2} = 60\\\\area \triangle ADC= \sqrt{60(60-40)(60-50)(60-30)} =600 cm^2$

For Δ ABC a=28 , b=30 , c= 26

$s=\dfrac{28+30+26}{2} = 42\\\\ar \triangle ABC= \sqrt{42(42-28)(42-30)(42-26)} = 336 cm^2$

Area of ABCD = ar Δ  ADC + ar Δ ABC= 600 + 336= 936 cm²

Hence, the area of quadrilateral ABCD is 936 cm²