23. Exemplar Exercise Problesm IX

1. The area of a regular hexagon of side \(a\) is the sum of the areas of the five equilateral triangles with side \(a\). 

 

2. The cost of levelling the ground in the form of a triangle having the sides \(51 m\), \(37 m\) and \(20 m\) at the rate of \(Rs.3\) per \(m^2\) is \(Rs.918\).

 

3. In a triangle, the sides are given as \(11 cm\), \(12 cm\) and \(13 cm\). The length of the altitude is \(10.25 cm\) corresponding to the side having length \(12 cm\).