Question

Area of the parallelogram $ABCD=1024$ sq. units. Find the area of $△AGH$. Here $E,F,G$ and $H$ are the mid points of $AB,AD,AE$ and $AF$ respectively.

• A. $32$ sq. units
• B. $64$ sq. units
• C. $100$ sq. units
• D. $120$ sq. units

Answer 1

The correct option is A

$32$ sq. units

Since, area of parallelogram $ABCD=1024$ sq. units, so,

area of $△ABD=\frac{1}{2}\times$ area of parallelogram $ABCD$ [Both have same base and are between same parallel lines]

$=\frac{1}{2}\times 1024=512$ sq. units

Now, $DE$ is the median of $△ABD$, so, it divides it into two triangles of equal area.

$\Rightarrow$ Area of $△ADE=\frac{1}{2}\times$ area of $△ABD$

$=\frac{1}{2}\times 512=256$ sq. units

Similarly, $EF$ is the median of $△ADE$ and divides it into two triangles of equal area.

$\Rightarrow$ Area of $△AEF=\frac{1}{2}\times 256=128$ sq. units

In this way, area of $△AGF=\frac{128}{2}=64$ sq. units

And finally, area of $△AGH=\frac{64}{2}=32$ sq. units