Posted by Sholanda on Monday, May 21, 2012 at 12:57am.
*These are regular polygons*
1.Find the area of a triangle with an apothem of 8 inches.
2.Find the area of a square with a radius of 12 inches.
3.Find the area of a pentagon with a hypotenuse of 10 inches.

Geometry  Reiny, Monday, May 21, 2012 at 8:32am
1. To be speaking of an "apothem" of a triangle, the triangle must be equilateral.
The apothem is the distance from the centre (centroid) to a side, and the apothem must be 1/3 of the length of the median
so the median is 24 inches, which makes the height 24 inches.
then by knowing the ratio of sides of the 306090 triangle, the side must be 48/√3
area = (1/2)(48/√3)(24) = 576/√3 square inches
2. We don't speak of a square having a radius.
Did you mean diameter?
if so let each side of square be x
x^2 + x^2 = 12^2
x = √98 =
area = x^2 = 98
3. Again, where does a hypotenuse come from in a pentagon?
Did you mean diagonal?
Find the internal angle. (you should get 108°)
From that you should be able to find all kinds of angles, depending on which lines you sketch.
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