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 30-60-90 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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