91Ó°ÊÓ

In Exercises 17 to \(30,\) use the formula \(A=\frac{1}{2} a P\) to find the area of the regular polygon described. In a regular octagon, the approximate ratio of the length of an apothem to the length of a side is \(6: 5 .\) For a regular octagon with an apothem of length \(15 \mathrm{cm},\) find the approximate area.

In a circle whose radius has length \(12 \mathrm{m},\) the length of an arc is \(6 \pi \mathrm{m}\). What is the degree measure of that arc?

At the Pizza Dude restaurant, a 12 -in. pizza costs \(\$ 3.40\) to make, and the manager wants to make at least \(\$ 2.20\) from the sale of each pizza. If the pizza will be sold by the slice and each pizza is cut into 6 pieces, what is the minimum charge per slice?

At the Pizza Dude restaurant, pizza is sold by the slice. If the pizza is cut into 6 pieces, then the selling price is \(\$ 1.25\) per slice. If the pizza is cut into 8 pieces, then each slice is sold for \(\$ 0.95 .\) In which way will the Pizza Dude restaurant clear more money from sales?

In Exercises 17 to \(30,\) use the formula \(A=\frac{1}{2} a P\) to find the area of the regular polygon described. In a regular polygon of 12 sides, the measure of each side is 2 in., and the measure of an apothem is exactly \((2+\sqrt{3})\) in. Find the exact area of this regular polygon.

A square yand is a square with sides 1 yard in length. a) How many square feet are in 1 square yard? b) How many square inclies are in 1 square yard?

The radii of two concentric circles differ in length by exactly 1 in. If their areas differ by exactly \(7 \pi\) in \(^{2},\) find the lengths of the radii of the two circles.

Use your calculator value of \(\pi\) unless otherwise stated. Round answers to two decimal places. The carpet in the circular entryway of a church needs to be replaced. The diameter of the circular region to be carpeted is \(18 \mathrm{ft}\). a) What length (in feet) of a metal protective strip is needed to bind the circumference of the carpet? b) If the metal strips are sold in lengths of 6 ft, how many will be needed?

The perimeter of a right triangle is \(12 \mathrm{m}\). If the hypotenuse has a length of \(5 \mathrm{m},\) find the lengths of the two legs.

Prove that the area of a trapezoid whose altitude has length \(h\) and whose median has length \(m\) is \(A=h m\)