Question

(I screenshot the question and choices) (plsss help me solve this <3 )

Answer 1

Ok, the formula to find the area of a regular polygon is...

A = 1/2 nsr

In this equation...

n = number of sides
s= side length
r = apothem (radius of the inscribed circle)

To find the area, we must first find the apothem. The apothem is the radius of the inscribed circle (draw a line from the center of the figure to the center of one of the sides). If you draw the apothem in to the figure, it creates a right triangle with a hypotenuse of 13.07 in and one side length of 5 in (1/2 of the figure's side length). Now we can find the apothem with the formula

a^2 + b^2 = c^2
a^2 = c^2 - b^2
a^2 = 13.07^2 - 5^2
a^2 = 170.8249 - 25
a^2 = 145.8249
a = 12.076

Now we have the value for the apothem and we can plug it into the area formula...

A = 1/2 nsr
(recall that n = number of sides; s= side length; r= apothem)

A = 1/2(8×10×12.076)
A = 40×12.076
A= 483.04 in^2

Rounded to the nearest tenth would be...

483.0 in^2