Find the area of the triangles abd and bcd using heron’s formula. hence find the area of quadrilateral abcd.

The Area of quadrilateral ABCD is 36 cm²  

Step-by-step explanation:

Given in the figure as :

ABD and BCD is a triangle

Length of sides of Δ ABD is:

AD = 3 cm

AB = 4 cm

BD = x =

Or, BD = = = 5 cm

Length of sides of ΔCBD is :

BC = 13 cm

CD = 12 cm

Now By Heron's formula

Area of triangle ABD =

And  s =

Or,    s =

Or,    s = 6 cm

∴ Area of triangle ABD =

Or, Area of triangle ABD = = 6 cm²          

Similarly  The area of  Triangle CBD =      

And  s =

Or,    s =

Or,    s = 15 cm

∴ Area of triangle CBD =

Or, Area of triangle CBD = = 30 cm²      

The Area of quadrilateral ABCD = Area Δ ABD + Area Δ CBD      

Or,The Area of quadrilateral ABCD =  6 cm²   +  30 cm²  = 36 cm²        

Hence The Area of quadrilateral ABCD is 36 cm²    Answer                                                    

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