Question

A regular hexagon has a perimeter of 60 in. What is the hexagon's area?

Answer 1

Divide the perimeter by 5 since it is regular. 60/5 = 12. Split the hexagon into a triangle and a rectangle. Find the area of each and add them together. Area of the rectangle is 12*12 = 144. To find the area of the triangle, you need to find an angle measure= y, hypotenuse = c, and a leg = a or b. An easy way to find an angle measure is to cut down the altitude and find the angle next to the base and altitude which would be 90° due to the fact that the triangle is regular also. With the regular triangle split in half, you have two right angle which form both 90-45-45 triangles. Use this formula, $A=ac \frac{siny}{2}$ --- $A=12*12 \frac{sin45}{2}$ to find the area of the triangle which equals to 50.91. Add (((144+50.91 = 194.91))) I hope I got this right if not, i'm sorry lol.