Geometry Difficult

A traffic signal board, indicating  'SCHOOL AHEAD' is an equilateral triangle with side ‘a'. Find the area of the signal board, using Heron's formula. If its perimeter is 180 cm, what will be the area of the signal board?

An isosceles triangle has a perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

A rectangular plot is given for constructing a house, having a measurement of 40 m long and 15 m in the front. According to the laws, a minimum of 3 m, wide space should be left in the front and back each and 2 m wide space on each of the other sides. Find the largest area where houses can be constructed.