Chapter 14.6, Problem 22PSD

To determine

To construct thetriangle with three medians.

Explanation of Solution

Given:

The three medians.

Calculation:

The equilateral triangle whose area is equal to that of hexagon can be constructed as follows-

Step 1- First draw the first median.

Step 2- It is known that the medians trisect each other and the point of intersection is called as the centroid of the triangle.

Step 3- Now, from the centroid draw two other medians and extend them till they join.

Step 4- Draw the circle taking the centroid as the center of the circle.

Step 5- Join all the vertices to get the required triangle with three medians as follows.