Posted by
**Kate** on
.

The area of a regular pentagon with a perimeter of 35 units.

Join the centre to each vertex to form 5 eq

Join the centre to each vertex to form 5 equal triangles. Consider one of those triangles

the central angle is 72º and each of the other two equal angles is 54º, and the base is 7 units.

Can you find the height of that triangle using simple trig?

then the area of the triangle is 1/2 base*height

Multiply that answer by 5.

I am not sure what the formula is for the height in my Trig book it says H=a sin 0... but i don't know what a is equal to.

O never mind sorry i was making the problem to hard then what it was

I would use tangent

let the height be h

then tan 54=h/3.5

h=3.5*tan54

=4.817

the formula your book uses requires the hypotenuse of the right-angled triangle.

O i did sin 36/3.5 =sin54/c

then a= .5(7)(4.8)= 16.8 units^2

then times 16.8*5=84ft squared

good, I had the same answer (84.3)