Question

Question 9
If a triangle and a parallelogram are on the same base and between same parallels, then the ratio of the area of the triangle to the area of the parallelogram is:

A) 1:3
B) 1:2
C) 3:1
D) 1:4

Answer 1

The answer is B.
Consider the following figure of parallelogram ABCD and triangle BCE that share the same base and are between same parallels.


Now, draw a perpendicular EF onto the base BC as shown in the figure.This EF is the height of the triangle and also is the height of the paralellogram(since, triangle and parallelogram are between the same parallels, their altitude will be same)

Area of triangle
$=\frac{1}{2}\times base\times height$ = $\frac{1}{2}\times BC\times EF$

Area of parallelogram
$=base\times height=BC\times EF$

$\Rightarrow \frac{Areaoftriangle}{Areaofparallelogram}=\frac{1}{2}$

$\therefore$ Area of triangle : Area of parallelogram = 1:2