How do we construct a triangle equal in area to a given triangle or quadrilateral?
1 Answer
Apr 24, 2018
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
- A straight line PQR parallel to base BC is drawn with the help of a ruler and a compass.
- 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 ofDeltaABC
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
- The diagonal
BD is drawn. - A straight line CX parallel to BD is constructed with the help of a ruler and a compass.
- AD is produced to intersect CX produced at E.
B,E are joined. DeltaABE will be required triangle.