Question

The line segment shown divide parallelogram ABCD into 8 regions and areas of the orange triangles are 48 21 and 63. Find the area of the blue triangle

Answer 1

you didn't attach figure . figure is shown below .
Here you see, area of ∆ADE = area of ∆ABF [ The two triangles ADE and ABF each have a height and a base side in common with the parallelogram, so that their areas are both equal to half the parallogram area ]

∴ area of ∆ADE = area of ∆ABF = 1/2 area of ABCD
We Indicated the regions by A₁ , A₂ , A₃ , A₄ and A₅ as shown in 2nd figure.
Here you see, ar(∆ADE) = A₁ + A₂ + A₃
ar(∆ABF) = A₃ + A₄ + A₅
But ar(∆ABE) = ar(∆ADE)
∴A₃ + A₄ + A₅ = A₁ + A₂ + A₃
⇒ A₅ = A₁ + A₂ - A₄
= 48 + 21 - 63
= 69 - 63 = 6

Hence, area of blue triangle = 6 sq unit