Question

Paralallelogram $ABCD$, triangle $ABE$ and rectangle $ABFG$ are on the same base $AB$ and between same parallel lines. Area of parallelogram is ${}^{\prime }{p}^{\prime }$, area of triangle is ${}^{\prime }{t}^{\prime }$ and area of rectangle is ${}^{\prime }{r}^{\prime }$. Find the relation between $p,t$ and $r$.

• A. $p=r=t$
• B. $p=r=2t$
• C. $p=r=\frac{t}{2}$
• D. $p=\frac{R}{2}=\frac{t}{2}$

Answer 1

The correct option is B

$p=r=2t$

Parallelogram $ABCD$ and Rectangle $ABFG$ are on the same base $AB$ and between same parallel lines.

Hence, their areas are equal, i.e. $p=r$ ... (i)

If a triangle and a parallelogram are having same base and between same parallel lines then aarea of the parallelogram is twice the area of the triangle.

$\Rightarrow p=2t$ ... (ii)

Similarly,

$r=2t$ ... (iii) ($\because$ Rectangle is also a parallelogram)

From (i), (ii) and (iii):

$p=r=2t$