Question

Refer to the following figure. If we were given the coordinates of A, E and B and the lengths of ED, DC and BC, how would you go about finding the area of this figure, pick the easiest way.

• A. Break the fig. into $\Delta$AEB and trapezium EBCD
• B. Break the fig. into $\Delta$AEB, $\Delta$EAB and $\Delta$BDC
• C. Break the fig. into trapeziums EDAX and AXCB where X is
  a point on DC such that AX is perpendicular to AX.
• D. Cant say

Answer 1

The correct option is A

Break the fig. into $\Delta$AEB and trapezium EBCD

Since we have the vertices of $\Delta$AEB, we can easily find the area of this shape. Now since the
trapezium sides are given, area can be found out very easily.
If we divide the figure into three triangles, we will have to find the sides of each triangle and then use Heron’s
formula which will be tedious though possible.
If we have to draw a perpendicular from A to CD at X, we will have to find the lengths of DX and XC to find the
areas of the trapeziums EDAX and AXCB and hence this will be much more complicated.
.