Sir/Madam would you please solve question no. 5

Sir/Madam would you please solve question no. 5 Its area. 5. ,4BCD is a parallelogram with side AB : 12 cm. Its diagonals AC and BD are of lengths 20 cm and 16 cm respectively. Find the area of gm ABCD.

AB =CD=12 cm .

And the diagonals bisect each other at the point of intersection.

So DO=BO=8cm (see below the actual diagram)

And AO=OC=10 cm 

So we now know that the three sides of Triangle ABO are 8 cm,10cm,12 cm .

So the perimeter is 8+10+12cm=30 cm

So half the perimeter is 15 cm

Now we can apply Heron’s formula.

So the area of triangle OAB is sqrt [15×(15–8)(15–12)(15–10)] 

=15 sqrt7

Now let’s assume the height of ABCD is h cm and it passes through the point O.

Now we get that OF=h/2 cm

So we get that

1/2 × h/2 × 12=15 sqrt7

Or, h=5 sqrt7

So, the area of ABCD is

h × 12= 5 sqrt7 × 12 cm^2= 60 sqrt7 cm^2

So our answer is 60 sqrt7 cm^2.

Hope this helps.