Question

If D(-1/5,5/2),E(7,3),F(7/2,7/2) are the mid pionts of sides of a triangle ABC and find the area of triangle ABC

Answer 1

Given info : IfD(-1/5,5/2), E(7,3) , F(7/2,7/2) are the mid pionts of sides of a triangle ABC.

To find : the area of triangle ABC.

Solution : concept : if D, E and F area the midpoints of BC , CA , AB respectively,

area of ∆DEF = 1/4 × area of ∆ABC

Therefore area of ∆ABC = 4 × area of ∆DEF

Let's find area of ∆DEF

Here (-1/5, 5/2), (7, 3) and (7/2, 7/2)

ar(∆DEF) = 1/2[-1/5(3 - 7/2) + 7(7/2 - 5/2) + 7/2(5/2 - 3)]

= 1/2[-1/5 × -1/2 + 7 × 1 + 7/2 × -1/2 ]

= 1/2 [5/4 + 7 - 7/4]

= 1/2 [7 - 1/2 ]

= 1/2 × 13/2

= 13/4

Therefore the area of triangle ABC = 4 × area of triangle DEF = 4 × 13/4 = 13 sq unit