Answer:
[tex]238\ in^{2}[/tex]
Step-by-step explanation:
we know that
The radii divide the pentagon into five isosceles triangles each with a center angle of 360/5 = 72 degrees
so
The area of the regular pentagon is equal to the area of one isosceles triangle multiplied by 5
step 1
Find the area of one isosceles triangle
Applying the law of sines
[tex]A=\frac{1}{2}(10)(10)sin(72\°)=47.55\ in^{2}[/tex]
step 2
Find the area of the regular pentagon
[tex]47.55*(5)=237.76\ in^{2}[/tex]
Round to the nearest whole square inch
[tex]237.76=238\ in^{2}[/tex]
