Question

Draw a triangle and divide it into three triangles of equal area in various ways.

Answer 1

Let us assume the dimensions of the triangle as AB = 6 cm, BC = 5 cm and CA = 7 cm.

The steps of construction are as follows:

1) Draw a line segment AB of length 6 cm.

2) With A as the centre and 7 cm as the radius, draw an arc on the upper side of AB.

3) With B as the centre and 5 cm as the radius, draw an arc cutting the previously drawn arc at point C.

4) Join AC and AB.

ΔABC is the required triangle.

We need to divide the triangle into three triangles of equal area.

Let the triangle with area one-third of the area of ΔABC be ΔADC.

Height of both the triangles would be same.

Thus, we need to construct ΔADC such that AD = 2 cm.

Similarly, we need to construct another triangle with the same area on side AB.

The steps of construction are as follows:

1) With A as the centre and 2 cm as the radius, draw an arc on AB and name it as D.

2) Join DC.

3) With D as the centre and 2 cm as the radius, draw an arc on AB and name it as E.

4) Join CE.

Thus, ΔADC, ΔDEC and ΔEBC are triangles of equal area.

Similarly, we can construct triangles by taking AC or BC as the base.