# 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 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**

- 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.