Question

Question 3
The area of the parallelogram ABCD is $90c{m}^2$.
Find
a) ar (ABEF)
b) ar ($\Delta$ABD)
c) ar ($\Delta$BEF)

Answer 1

a) We know that parallelograms having same base and lying between same parallel lines will have equal area.
ABCD and ABEF are parallelograms having same base AB and lying between same parallel lines.

Therefore, Area of ABEF
$=90c{m}^2$

b) If a triangle and a parallelogram have the same base and lie between same parallel lines, then the area of the triangle will be half of the area of the parallelogram.
Therefore,
$ar\left(△ABD\right)=\frac{1}{2}\times ar\left(ABCD\right)=45c{m}^2$

c) $ar\left(△BEF\right)=\frac{1}{2}\times ar\left(ABEF\right)=45c{m}^2$