Question

INA QUADRILATERALABCDAB=28,BC=26CM=CD=50CM,DA=40CMAND DIAGONLAC=30 FIND THE AREA OF QUADRILATERAL

Answer 1

The quadrilateral can be divided into two triangles- ΔABC and ΔADC.
Now find the areas of the triangles and add them.

In ΔABC, AB= 28, BC = 26, AC = 30
s = (28+26+30)/2 = 84 / 2 = 42
$Area= \sqrt{s(s-a)(s-b)(s-c)} \\ Area= \sqrt{42(42-26)(42-30)(42-28)}\\ Area= \sqrt{42*16*12*14} \\Area= 336\ cm^2$

Similarly in ΔADC. AD = 40, CD = 50, AC = 30
s = (30+40+50)/2 = 60
applying same formula, 
$Area = \sqrt{60*30*20*10}=600cm^2$

Total area = 300+600 = 900 cm²