91Ó°ÊÓ

Find the exact circumference and area of a circle whose radius has length 8 cm.

Find the area of an equilateral triangle with a) sides of length \(2.5 \mathrm{m}\) each. b) apothem of length 3 in.

For a regular hexagon, the length of the radius is 12 in. Find the length of the radius for the inscribed circle for this hexagon.

In a particular type of regular polygon, the length of the radius is exactly the same as the length of a side of the polygon. What type of regular polygon is it?

Find the area of an equilateral triangle with apothem \(a=3.2 \mathrm{cm}\) and perimeter \(P=19.2 \sqrt{3} \mathrm{cm}\)

In Exercises 17 to \(30,\) use the formula \(A=\frac{1}{2} a P\) to find the area of the regular polygon described. Find the area of a regular pentagon with an apothem of length \(a=5.2 \mathrm{cm}\) and each side of length \(s=7.5 \mathrm{cm}\)

A trapezoid has an area of \(96 \mathrm{cm}^{2} .\) If the altitude has a length of \(8 \mathrm{cm}\) and one base has a length of \(9 \mathrm{cm},\) find the length of the other base.

For concentric circles with radii of lengths 3 in. and 6 in., find the area of the smaller segment determined by a chord of the larger circle that is also a tangent of the smaller circle.

The numerical difference between the area of a square and the perimeter of that square is \(32 .\) Find the length of a side of the square.

A circle can be inscribed in an equilateral triangle each of whose sides has length \(10 \mathrm{cm} .\) Find the area of that circle.