Is the area of a reg. decagon with a perimeter of 240, A=4431.86

Is the area of a reg. decagon with a perimeter of 240, A=4431.86? PLEASE HELP ME

A decagon with a perimeter of 240 has a side of 24. The angle between two consecutive radii is 36°

a/sin(72°) = 12/sin(18°) {Law of Sines, where a is the apothem}

a = 12sin(72°)/sin(18°) = 36.9322

A = 1/2aP = 1//2(36.9322)(240) = 4431.86. Good job! ☺

A decagon has 10 sides so that gives you 24 per side. If you take one chunk of the decagon (1 tenth of it), you will have an isosceles triangle with 24 on its base and an opposite angle of 36 degrees (360 degrees divided by 10).

Divide the isosceles triangle in two (that's 1/20 of the decagon) and you will have 12 on its base with and opposite angle of 18 degrees. Using tan theta = a/b where theta = 18 and a = 12, you will get b = 36.9322. The area of that triangle will then be 12*36.9322/2 = 221.5932

Multiply that by 20 and you will get 4431.864.

So yes, the area of a decagon that has a perimiter of 240 is 4431.86.