Question

In the given figure area of $\Delta DAC=45c{m}^2$, then find the area of rectangle ABEF.

• A. $22.5c{m}^2$
• B. $45c{m}^2$
• C. $80c{m}^2$
• D. $90c{m}^2$

Answer 1

The correct option is D $90c{m}^2$

Area of $\Delta DAC=45c{m}^2$ ......(given)

Diagonal AC divides the ||gm ABCD into two triangles of equal area.

Area of ||gm ABCD = 2 x Area of $\Delta DAC$
= $90c{m}^2$

In ABCD and ABEF, AB is common base and both of them are lying between the same parallel lines i.e., AB and ED.

$\because$ Two parallelograms having same base and between the same parallels are equal in area.

$\therefore$ Area of rectangle ABEF = area of parallelogram ABCD = 90 cm${}^2$