Question

What is the area of the parallelogram?

Answer 1

AEB is a right isoceles triangle. It means that it is half a square. So, AB is the diagonal of the square with side AE.

The side and diagonal of a square are linked by the following formula:

`d = l√(2)`

which means

`18√(2) = l√(2)`

and this AE=EB=18.

The area of a parallelogram is given by the multiplication of the base and the height, which in our case means

`A = \overline{BD}\cdot\overline{EB} = 18\cdot 28 = 504`

Answer 2

Triangle AEB is a 45 45 90 triangle

Ratio of leg:hypo = x:x√2

Given hypo AB = 18√2

so leg AE = BE = 18

Area of Parallelogram = bh

where b = 28 and b = 18

so

A = 28 * 18

A = 504 square units