Find the area of the regular polygon.

Question

Answer 1

draw the altitude which bisects the bottom base

you have two congruent right triangles

they are both 30-60-90 right triangles

the hypotenuse is 10

the shorter side, which is opposite the 30° angle, is half of the hypotenuse, therefore it is 5

however, we know this because we drew the altitude which bisects the base of 10

the longer side is always the shorter side times √3, or 5√3; this is the altitude

so, the altitude is 5√3 and the base is 10

A=(1/2)bh

A=(1/2)(10)(5√3)

A=25√3

Answer 2

Cut it in half; Now there's 2 rt triangles.

To get the height: a/sinα=b/sinβ=c.

In this case α=30 (cut the 60 in half); β=60 (given).

We want side "b"; the formula is ab=area. Again: b/sinβ=c=10.

So b/.866=10; b=8.66.

"a"is b/2=4.33

area=8.66*4.33=3.7949............

PS side "a" shortest

b mid

c hypotenuse