Question

Two parallelograms stand on equal bases and between the same parallels. The ratio of their areas is

• A. $1:2$
• B. $2:1$
• C. $1:1$
• D. $1:3$

Answer 1

Answer: (C)

$1:1$

Let area of first parallelogram be $P_1$

And area of second parallelogram be $P_2$

$\Rightarrow$ Area of parallelogram $=b\times h$

$\Rightarrow$ $P_1=b_1\times h_1$

$\Rightarrow$ $P_2=B_2\times h_2$

$\Rightarrow$ $b_1=b_2$ [ As per the question ]

$\Rightarrow$ $h_1=h_2$ [ As the distance between $2$ parallel lines is always equal ]

$\therefore$ $P_1=b\times h$ ------ ( 1 )

$\therefore$ $P_2=b\times h$

By equating ( 1 ) and ( 2 ) we get,

$\Rightarrow$ $P_1=P_2$

$\Rightarrow$ $P_1:P_2=1:1$