What is a rectangular pentagonal garden?
Where is point A ?
A rectangular pentagonal garden plot has centre of symmetry O and an area of 50m^2. Find the distance OA.
2 answers
I think we can safely assume that it's a "regular" pentagonal garden, and that OA is the apothem. If so, then the 5 isosceles triangles have a vertex angle of 72°
If we call the side length 2s and the apothem length a, then we have
s/a = tan36°
That makes the area of each isosceles triangle s*a = a^2 tan36°
The area of the pentagon is thus 5a^2 tan36°
Now we have
5a^2 tan36° = 50
OA = a = √(10 cot36°)
If we call the side length 2s and the apothem length a, then we have
s/a = tan36°
That makes the area of each isosceles triangle s*a = a^2 tan36°
The area of the pentagon is thus 5a^2 tan36°
Now we have
5a^2 tan36° = 50
OA = a = √(10 cot36°)
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