# Geometry

posted by .

*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 -

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.

## Similar Questions

1. ### Math

Find the area of a regular pentagon if its apothem is approximately 4 ft long and each of its sides are 5.8 ft long. So I tried dividing the pentagon into triangles...but then I came up with the answer 24.41?
2. ### Math/Geometry

Can you help me with this? Find the area of each regular polygon. Round to the nearest tenth. 1. an equilateral triangle with an apothem 8.9 inches long
3. ### Geometry

Problem : Howm do you find the area of a circle circumscribed about a regular pentagon with a perimeter of 50 inches. So far I each side of pentagon is 10. How do I find the radius of the circle?
4. ### geometry

in order to find the area of a regular hexagon using the formula Area=1/2(nxs)(a)you must frist find the apothem whie vertical leg of a 30-60-90 triangle with the base of 3. Find the length of the apothem in the 30-60-90 triangle
5. ### Geometry

Find the area of the regular polygon with the given radius. The radius of the square is 6 cm. area= apothem x perimeter/ 2
6. ### Geometry

Find the area of the regular polygon with the given radius. The radius of the square is 6 cm. area= apothem x perimeter/ 2
7. ### Geometry help

1. If a square has a radius of twelve, would its apothem be 6sqrt2?
8. ### Geometry

Regular pentagons A and B are similar. The apothem of Pentagon A equals the radius of Pentagon B. Compare the areas. The area of Pentagon A is equal to 1.49 times the area of Pentagon B. The area of Pentagon B is equal to 1.49 times …
9. ### Geometry

Please Please HELP!!!! I need the answer to this and i've worked it out but I don't know if it is correct... Please check my answer!!!! The polygons are regular polygons. Find the area of the shaded region to the nearest tenth. I can't …
10. ### Geometry

1.What is the perimeter of a rectangle with width 10 inches in length 13 inches?

More Similar Questions