How do we construct a triangle equal in area to a given triangle or quadrilateral?

Drawing triangle equal in area to a given triangle

Let ABC be the given triangle. We are to construct a triangle equal in area to this triangle.

Principle followed

The areas of all triangles of same base are same if they are placed in between two parallel sraight lines.

Steps

1. A straight line PQR parallel to base BC is drawn with the help of a ruler and a compass.
2. B and C may be joined with any point on the line PQR to get a triangle equal in area of triangle ABC. Here #DeltaPBC,DeltaQBC,DeltaRBC# are three triangles drawn , which are equal in area of #DeltaABC#

Drawing triangle equal in area to a given quadrilateral

Let ABCD be the given quadrilateral. We are to construct a triangle equal in area to this quadrilateral.

Principle followed

The areas of all triangles of same base are same if they are placed in between two parallel sraight lines.

Steps

1. The diagonal #BD# is drawn.
2. A straight line CX parallel to BD is constructed with the help of a ruler and a compass.
3. AD is produced to intersect CX produced at E. #B,E# are joined.
4. #DeltaABE# will be required triangle.