Question

Area of the parallelogram $ABCD=800$ sq. units. Find the area of $△AFC$. Here, $E$ and $F$ are the mid points of $AB$ and $AE$ respectively.

• A. $100$ sq. units
• B. $125$ sq. units
• C. $75$ sq. units
• D. $50$ sq. units

Answer 1

The correct option is A $100$ sq. units

Join the the vertices $D$ and $B$

Diagonal $BD$ divides the parallelogram $ABCD$ into two triangles of equal area.

$\Rightarrow Areaof△ABD=\frac{1}{2}\times areaofparallelogramABCD$

$=\frac{1}{2}\times 800=400sq.units$

Given, E is the midpoint of AB
$\Rightarrow$ $DE$ is the median of $△ABD$ and it divides the triangle into two triangles of equal area.

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

$=\frac{1}{2}\times 400=200$ sq. units

Similarly, $DF$ is the median of $△ADE$,

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

$=\frac{1}{2}\times 200=100$ sq. units

Now, area of $△AFD=$ area of $△AFC$ [Triangles on same base and between same parallel lines]

$\Rightarrow$ Area of $△AFC=100$ sq. units