Question

the surface of soccer ball is made of a pattern of regular pentagons and hexagons .If each hexagon on a soccer ball has perimeter of 9 inches , what is the area of a hexagon?

Answer 1

Hexagon is made up of 6 equilateral triangles.
Since they are equilateral and the perimeter is 9 inches, then each side must be 3
Area of a triangle is 1/2 b h
we need to find the height
by drawing the height of an equilateral it would create a right triangle
the hypotenuse would be 3
the bottom leg would be 1 1/2
to find the height you use the pythagorean theorem
a^2 + b^2 = c^2
(3/2)^2 + b^2 = 3^2
9/4 + b^2 = 9
b^2 = 6 3/4 = 27/4
b = 3 sqrt(3) over 2

Area would be
1/2 * 3 * 3sqrt(3)/2

9sqrt(3)
-------
4

then you have 6 of these triangles.

6 * 9 sqrt(3)
--------
4

27 sqrt(3)
--------
3

Answer 2

thank