Question

The mid-points of the sides of a triangle ABC along with any of the vertices as the fourth point make a parallelogram of area equal to what?

Answer 1

equal to the half of area of whole triangle

Answer 2

The midpoints of all sides of a triangle and the fourth point is extended to any vertex.

Please draw the figure.

Lets take the triangle to be ABC.

The midpoints are:

D...........on AB

E..............on BC

F...............on AC

I join the fourth point to A.

So the parallelogram is DEFA.

Now note that the parallelogram has a diagonal DF.

Draw DF .

You will see that DF divides the parallelogram into two congruent triangles each of equal area.

These triangle are also equal to:

triangle DEB and triangle EFC

Hence the triangle ABC has four equal triangles within it.

Now the parallelogram makes 2 of these triangles.

So obviously the area of the parallelogram will be half of that of the triangle ABC.

DEFA area=1/2*area ABC.

Hope it helps.