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)

Great job!

To find the height of the triangle, you can use the tangent function. Let the height be denoted as h. We know that one of the angles in the triangle is 54 degrees, and the opposite side is h, while the adjacent side is half the base, which is 7 units. So, we have tan(54°) = h/3.5.

Solving for h, we can rewrite the equation as h = 3.5 * tan(54°). Using a calculator, we find that h is approximately 4.817 units.

To find the area of the triangle, you can use the formula A = (1/2) * base * height. Substituting the values, we have A = (1/2) * 7 * 4.817 = 16.8245 square units.

Since there are 5 equal triangles in the regular pentagon, we can multiply the area of one triangle by 5. So, the total area of the pentagon will be 16.8245 * 5 = 84.1225 square units, which can be approximated as 84.3 square units.