Question 1006573: find the lengths of the apothem and the radius of a square whose sides have length 10in ?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! For any square, the apothem is always half as long as the side length
apothem = (1/2)*(side length)
apothem = (1/2)*(10)
apothem = 5
The apothem is 5 units long. The apothem is the segment starting at the center of the regular polygon and it stretches to the midpoint of any side of the regular polygon.
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If you draw out the square, add in the apothem and radius, you'll see a right triangle form.
This right triangle has legs of 5 and 5. The hypotenuse is unknown. Let's call it x for now
Pythagorean theorem:
a^2 + b^2 = c^2
5^2 + 5^2 = x^2
25 + 25 = x^2
50 = x^2
x^2 = 50
x = sqrt(50)
x = sqrt(25*2)
x = sqrt(25)*sqrt(2)
x = 5*sqrt(2)
So the radius of the square is 5*sqrt(2)
The radius of a regular polygon (aka the circumradius) is the segment going from the center to any vertex of the regular polygon.
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Answers:
Apothem = 5 inches
(circum)radius = 5*sqrt(2) inches
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