Math mini-contest trigonometry problem for Day 6 on D.Buzz for May 2021 😎

in D.Buzz β€’ 2 months ago

Math mini-contest problem for Day 6 on D.Buzz for May 2021 😎

Holovision needs to design a 50-sided regular polygon for his new holographic project. Given any four consecutive vertices EFGH, the distance of E from H is 36 centimeters. What is the area of the polygon?

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This is a tough one!
Here's my try:
EFGH covers 3 triangles of the polygon. The polygon angle covered by EFGH is alpha = 3/50*2pi. The center of the polygon to point E to the middle of line EH is a right angle triangle, which allows me to calculate the "radius" r from the center to E as (36/2) / sin(alpha/2) = 96.06. The polygon consists of 50 isosceles triangles with angle alpha/3 and side length r
=> Area = 50 * r^2 * sin(alpha/3) / 2 = 28913.37 cm^2