Exam 9: Areas of Polygons and Circles

In ,     and     . How are and related?

Where C is the circumference of a circle and r is its length of radius, the approximate value of the ratio C : r is:

If a sector of a circle has arc measure 120°, then its area equals one-third the area of the circle.

For the right triangle with sides of lengths 5 in, 12 in, and 13 in, find the length of the radius of the inscribed circle.

For a regular octagon, the length of the apothem is a = 8.2 cm while the length of each side is s = 6.7 cm. To the nearest tenth of a square centimeter, find the area of the regular octagon.

If m = 50 ° , then what fraction of the area of the circle represents the area of the sector shown?

For a triangle whose perimeter measures 36 units, the radius of the inscribed circle is 3.Find the area of the triangle.

If the area of a regular octagon is 25 , find the area of the regular octagon whose sides are twice those of the first octagon.

In , a sector is bounded by radii and and arc . If m = 90 ° and PX = 6 m, find the exact area of the sector.

For a regular pentagon, find the measure of each central angle.

If m = 45 ° and OA = 4.3 cm, find l correct to the nearest tenth of a centimeter.

Find the area of the triangle whose sides have lengths 13 cm, 14 cm, and 15 cm.

The region bounded by chord and arc is known as a segment of the circle.

If , then the altitude to base of is .

If both a parallelogram and triangle have the same base and altitude, then thearea of the parallelogram is twice the area of the triangle.

In , m = 45 ° and OA = 6 cm. Find .

The area of an equilateral triangle with sides of length s is given by A = .

Assuming that     and     in , what line segment is the altitude of this parallelogram with respect to side ?

In , m = 90 ° . What fraction represents the part of the circumference that is the length of ?

The area of is 35.1 . Choosing a side of RSTV that measures 4.5 cm as the base, what is the length of the corresponding altitude?