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Lesson 11.3 Key Terms Area of a Regular Polygon: Area of a Circle:

Example 3-1a Find the area of a regular pentagon with a perimeter of 90 meters.

Example 3-1a Apothem: The central angles of a regular pentagon are all congruent. Therefore, the measure of each angle is or 72. is an apothem of pentagon ABCDE. It bisects and is a perpendicular bisector of. So, or 36. Since the perimeter is 90 meters, each side is 18 meters and meters.

Example 3-1a Write a trigonometric ratio to find the length of. Use a calculator. Divide each side by tan. Multiply each side by GF.

Example 3-1a Simplify. Area: Area of a regular polygon Answer:The area of the pentagon is about 558 square meters.

Example 3-1b Find the area of a regular pentagon with a perimeter of 120 inches. Answer:about

Example 3-2a An outdoor accessories company manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square yards. The diameter of the umbrella is 72 inches, and the cover must extend 8 inches in each direction. So the diameter of the cover is or 88 inches. Divide by 2 to find that the radius is 44 inches.

Example 3-2a The area of the cover is square inches. To convert to square yards, divide by Answer:The area of the cover is 4.7 square yards to the nearest tenth. Area of a circle Substitution Use a calculator.

Example 3-2b A swimming pool company manufactures circular covers for above ground pools. If the cover is 10 inches longer than the pool on each side, find the area of the cover in square yards. Answer:

Example 3-3a Find the area of the shaded region. Assume that the triangle is equilateral. Round to the nearest tenth. The area of the shaded region is the difference between the area of the circle and the area of the triangle. First, find the area of the circle. Area of a circle Substitution Use a calculator.

Example 3-3a To find the area of the triangle, use properties of 30  -60  -90  triangles. First, find the length of the base. The hypotenuse of so RS is 3.5 and. Since.

Example 3-3a Use a calculator. Area of a triangle Answer:The area of the shaded region is – 63.7 or 90.2 square centimeters to the nearest tenth. Next, find the height of the triangle, XS. Since m 3.5

Example 3-3b Find the area of the shaded region. Assume that the triangle is equilateral. Round to the nearest tenth. Answer: 46.0 in 2