Find the area of the figure. Round to the nearest tenth if necessary.

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Presentation transcript:

Find the area of the figure. Round to the nearest tenth if necessary. Lesson 3 Menu

Find areas of regular polygons. Find areas of circles. apothem Lesson 3 MI/Vocab

Lesson 3 KC1

Area of a Regular Polygon Find the area of a regular pentagon with a perimeter of 90 meters. Lesson 3 Ex1

Area of a Regular Polygon 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. Lesson 3 Ex1

Area of a Regular Polygon Write a trigonometric ratio to find the length of . Multiply each side by GF. Divide each side by tan . Use a calculator. Lesson 3 Ex1

Area of a Regular Polygon ≈ 557 Simplify. Answer: The area of the pentagon is about 557 square meters. Lesson 3 Ex1

Find the area of a regular pentagon with a perimeter of 120 inches Find the area of a regular pentagon with a perimeter of 120 inches. To the nearest square inch. A. 890 in2 B. 1225 in2 C. 991 in2 D. 1982 in2 A B C D Lesson 3 CYP1

Lesson 3 KC2

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 8 + 72 + 8 or 88 inches. Divide by 2 to find that the radius is 44 inches. Lesson 3 Ex2

Area of a circle Substitution Use a calculator. The area of the cover is 6082.1 square inches. To convert to square yards, divide by 1296. Answer: The area of the cover is 4.7 square yards to the nearest tenth. Lesson 3 Ex2

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. A B C D A. 31.0 yd2 B. 33.8 yd2 C. 1215.1 yd2 D. 43743.5 yd2 Lesson 3 CYP2

Area of an Inscribed Polygon 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. Lesson 3 Ex3

Area of an Inscribed Polygon 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 SZ . Since . Δ Lesson 3 Ex3

Area of an Inscribed Polygon Next, find the height of the triangle, XS. Since m 3.5 Area of a triangle Use a calculator. Answer: The area of the shaded region is 153.9 – 63.7 or 90.3 square centimeters to the nearest tenth. Lesson 3 Ex3