Find the side, radious, perimeter, and area of a square with apothem = 10.
My book describes it very vaguely. I really need help on this one.
2007-08-14 11:56:35 · 5 answers · asked by Nick? 2 in Science & Mathematics ➔ Mathematics
The apothem of a square is the distance from the center of the square perpendicular to a side. The apothem is thus 1/2 the side and so a side = 20
The perimeter is 4*side = 4*20 = 80.
The area is side^2 = 20^2 = 400 units^2.The diagonal is 20*sqrt(2). A square does not have a radius.
2007-08-14 12:04:25 · answer #1 · answered by ironduke8159 7 · 1⤊ 1⤋
The apothem is the distance from the center to a side.
So, a side would be twice the apothem or 10 x 2 = 20.
The radius is the distance from the center to a corner.
You need to use pythagorean theorom for this:
a^2 + b^2 = c^2, where a is the apothem, b is half a side and c is the radius
r^2 = 10^2 + 10^2
r = sqrt(100 + 100)
r = sqrt(2(100))
r = 10sqrt(2)
= 14.14
The perimeter is the sum of the sides = 20 + 20 + 20 + 20 = 80.
The area is the product of 2 sides = 20 x 20 = 400.
2007-08-14 12:05:50 · answer #2 · answered by Larry C 3 · 0⤊ 0⤋
If an apothem is a segment from the center of the polygon to one of it's sides, doesn't that make the total side 20 units?
So the side would be 20 and the perimeter would be 80 and the area would be 400 sq units.
Radius? Of a square?
2007-08-14 12:06:46 · answer #3 · answered by Anonymous · 0⤊ 0⤋
the radius is 10...
the side will be 20, the area will be 100.
apothem means perpendicular distance from center to edge of a polygon
2007-08-14 12:01:13 · answer #4 · answered by CyEngin 2 · 1⤊ 3⤋
side=10
radious=5
area=10*10=100
perimeter=4*10=40
2007-08-14 12:05:37 · answer #5 · answered by Anonymous · 0⤊ 1⤋