what is the area of a pentagon if the perimeter is 1000 metres? please show working out?

Answer 1

5 equal sides. Each side is 200 meters.
The pentagon can be dissected into 10 right triagles each having 36 degrees as an adjacent angle and a adjacent length of 200/2 = 100 meters
The opposite side of the triangle will equal the apothem of the pentagon.
COTANGENT(angle) = OPP/ADJ
OPP= ADJ*COT(a)
The area of a pentagon is A=1/2 (perimeter)*(apothem)
A= 1/2 (1000)*(cot(36)*100)

Answer 2

A = .5aP, wher a is apothem and P is perimeter
a = side/2 cot36 = 200/2cot36= 100 cot 36
So area = A = .5*1000*100cot36= 50,000cot36 m^2