Question

Triangle EGF is right angled triangle such that angle EFG is 90. EF = 5cm and EG = 13 cm,
then area of triangle EPQ where p and q are the mid-points of EF and EG respectively,is:

I know the answer its 15/2 square cm but I want steps. Please dude answer me.

Answer 1

EF=5cm⇒EP=2.5cm (∵ P is midpoint of EF )

EG=13cm⇒EQ=6.5cm (∵ Q is midpoint of EG )

PQ²=(6.5)²-(2.5)²=42.25-6.25=36cm

(∵ EPQ forms a right-angled triangle , right-angled at P)

∴PQ=6cm

Area of ΔEPQ =1/2×bh

                        = 1/2×6×2.5

                        = 15/2 cm²