Decagon Side Length
Geometry
Level
1
2 regular decagons (10-sided) have sides lengths 16 cm and 30 cm. A third regular decagon has area that is equal to the sum of areas of the other 2 decagons. What is the side length (in cm) of the third regular decagon?
The answer is 34.
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1 solution
A1+A2=A3
0.5 sin(360/10) 16^2+0,5sin(360/10) 30^2=0,5sin(360/10)*r^2 (both sides divided by 0.5sin(360/10)
we get 16^2+30^2=r^2
r=34