+129852 Both triangles PNQ and LPQ have the same altitude ( PQ)
So....triangles under the same altitude are to each other as their bases...and since the area of LPQ is twice that of PNQ...its base (PL) must be twice as long as the base of PNQ = (NP)
Therefore....PL = 2NP
And since PQ is parallel to LM ⇒ NL : NP = LM /PQ = [ NP + PL ] / NP = [NP + 2NP] / NP = 3NP / NP = 3
Therfore...LM : PQ = 3 : 1
So...the scale factor of triangle NLM to triangle NPQ is 3 : 1 = 3
And the area of triangle NLM = Area of triangle NPQ * scale factor^2 = 8 * 3^2 = 8 * 9 = 72 units^2
So.... Area of LQM = [ area of NLM - combined areas of (PNQ + LPQ) ]
72 - [ 8 + 16 ] =
72 - 24 =
48 units^2
