Question

Draw a regular pentagon so that it has a perimeter of 20 cm. Use the Regular Polygon Area Conjecture and a centimeter tyler to find its approximate area.

Answer 1

Check the graph below.
`Area = 27.52 cm^(2)`

Explanation:

A Regular Pentagon has an interior angle of 108º an an exterior angle of 72º.

Since the perimeter is 20 cm, let's draw it respecting it those properties, besides all of the three sides must have the same measure.

And since we can divide it, into three triangles, we can calculate the area using tangent.

So, let's find out the area:

`A_5=(s^(2)n)/(4tan((180)/(n))) =(4^(2)*5)/(4tan(180)/(5))\\ \\A\approx27.52cm^(2)`

So check it down