ABCD is an isosceles trapezoid with AB as its longest side and O divides the diagonals AC and BD in the ratio of 1:2. What is the area of ABCD if the area of BOC is 2 square meter?

Answer 1

If AB is the longest side, then O cannot divide AC and BD in the ratio 1:2 since mAB>mDC.

We will use A(BOC) to represent the area of triangle BOC, and so on.

Draw a diagram of the trapezoid ABCD with AB//DC and AB>DC. The diagonals AC and BD meet at O.

If the division is 2:1,
then
A(BOC)=2 (given)
A(COD)=1 (same height, ratio of base)
A(DOA)=2 (congruent with BOC)
A(AOB)=4 (same height as DOA, ratio of sides).
Add up the area of each of the four triangles to get the area of the trapezoid.