91Ó°ÊÓ

Two circles have radii \(6 \mathrm{cm}\) and their centers are, \(6 \mathrm{cm}\) apart. Find the area of the region common to both circles.

Use a calculator or the trigonometry table to find the area of each trapezoid to the nearest tenth. An isosceles trapezoid with bases 12 and 16 is inscribed in a circle of radius \(10 .\) The center of the circle lies in the interior of the trapezoid. Find the area of the trapezoid.

A path \(2 \mathrm{m}\) wide surrounds a rectangular garden \(20 \mathrm{m}\) long and \(12 \mathrm{m}\) wide. Find the area of the path.

A room 28 ft long and 20 ft wide has walls 8 ft high. a. What is the total wall area? b. How many gallon cans of paint should be bought to paint the walls if 1 gal of paint covers \(300 \mathrm{ft}^{2}\) ?

Draw an equilateral triangle and its inscribed and circumscribed circles. Find the ratio of the areas of these two circles.

A wooden fence 6 ft high and 220 ft long is to be painted on both sides. a. What is the total area to be painted? b. A gallon of a certain type of paint will cover only \(200 \mathrm{ft}^{2}\) of area for the first coat, but on the second coat a gallon of the same paint will cover \(300 \mathrm{ft}^{2}\). If the fence is to be given two coats of paint, how many gallons of paint should be bought?

The lengths of the sides of three squares are \(s, s+1,\) and \(s+2\) If their total area is \(365 \mathrm{cm}^{2},\) find their total perimeter.

A regular octagon is inscribed in a circle with radius \(r\) Find the area enclosed between the circle and the \(r . \quad\) Use \(\quad \pi \approx 3.14\) and octagon in terms of \(\sqrt{2} \approx 1.414\).

a. An equilateral triangle has sides of length \(s\). Show that its area is \(\frac{s^{2}}{4} \sqrt{3}\) b. Find the area of an equilateral triangle with side 7 .

A regular polygon with apothem \(a\) is inscribed in a circle with radius \(r\) a. Complete: As the number of sides increases. the value of \(a\) gets nearer to \(\underline{?}\) and the perimeter of the polygon gets nearer to \(2 \pi r .\) b. In the formula \(A=\frac{1}{2} a p,\) replace \(a\) by \(r,\) and \(p\) by \(2 \pi r .\) What formula do you get?