# Geometry

posted by .

How do you find the apothem of a regular pentagon? Hexagon?

• Geometry -

If I recall, apothem is the distance from the centre to the midpoint of a side
so look at one of the equal 5 isosceles triangles.
the central angles are 360/5 or 72° each, making the base angles 54°.

let the base be length x
then
tan 54° = apoth/(x/2)
apothem = (1/2) base x tan 54°

## Similar Questions

1. ### geometry

Find the area of a regular pentagon with side equal to 3 and apothem equal to K.
2. ### Geometry

the side of a regular hexagon is twice the square root of its apothem. find the apothem and side length.
3. ### Geometry

Find the area of a circle circumscribed about a regular hexagon with an apothem of 5 inches. Round to the nearest tenth
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

Hi, I'm having a difficult time understanding a couple of Geometry questions on my homework and I'd really appreciate it if someone could answer them and explain to me how to get the same answer. Question 1: A regular pentagon has …
6. ### Geometry

Assume each side of the hexagon is worth 10 units. Calculate the apothem, using the fact that it is part of a special triangle to get the answer exactly. Then use the exact value of the apothem to calculate the area of the hexagon.
7. ### Geometry

what is the relationship between the side length and the apothem in a regular hexagon?
8. ### geometry

a regular pentagon has an apothem of 3.2 and an area of 37.2 cm. What is the length of one side of the pentagon?
9. ### 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 …
10. ### math

the area of a regular hexagon is given as 384√3 a. how long is each side of a hexagon b. find the radius of a hexagon c. find the apothem of a hexagon

More Similar Questions