Question

If ABDC is a parallelogram of area 132 cm${}^2$ and E, F are mid points of AB and CD respectively then the area of parallelogram AEFC is ____

• A. 60 cm${}^2$
• B. 66 cm${}^2$
• C. 132 cm${}^2$
• D. can't be found

Answer 1

The correct option is B 66 cm${}^2$

Given, area of parallelogram ABDC is 132 cm${}^2$
and E, F are mid points of AB and CD
$\because$ Area of parallelogram is base $\times$ height
Area of ABDC = CD $\times$ EG
$\Rightarrow$ CD $\times$ EG = 132 cm${}^2$-----(1)
Area of AEFC = CF $\times$ EG
$\because$ CF = $\frac{1}{2}$CD
$\Rightarrow$ Area of AEFC = $\frac{1}{2}$CD$\times$ EG
= $\frac{1}{2}$ $\times$ 132 cm${}^2$
= 66 cm${}^2$