Question

In the diagram below, the areas of the triangles are as follows: A1=1024, A2=1016, A3=1057. What is the area of A4?

Answer 1

First we will use triangles with the areas A1 and A3:

A1 = a · h1 / 2   and A3 = a · h2 / 2,   where h1 + h2 = b

Then:  h2 = b - h1

1024 = a · h1 / 2              1057 = a · ( b - h1 ) / 2

( we multiply both sides of the equations by 2 )

2048 = a · h1                   2114 = a b - a h1

Therefore:  2114 = a b - 2048

a b = 2048 + 2114 = 4162

And the area of the rectangle is A(total) = a b

A4 = A(total) - ( A1 + A2 +A3 ) = 4162 - ( 1024 + 1016 + 1057 ) =

= 4162 - 3097 = 1065

Answer: The area of A4 is 1065.