1 / 6

Find the area of a regular polygon with 10 sides and side length 12 cm.

Find the perimeter p and apothem a , and then find the area using the formula A = ap. 1 2. 360 10. Because the polygon has 10 sides, m ACB = = 36.

rhea-tyson
Download Presentation

Find the area of a regular polygon with 10 sides and side length 12 cm.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Find the perimeter p and apothem a, and then find the area using the formula A = ap. 1 2 360 10 Because the polygon has 10 sides, mACB = = 36. and are radii, so CA = CB. Therefore, ACMBCM by the HL Theorem, so m ACM = m ACB = 18 and AM = AB = 6. CA CB 1 2 1 2 Trigonometry and Area LESSON 10-5 Additional Examples Find the area of a regular polygon with 10 sides and side length 12 cm. Because the polygon has 10 sides and each side is 12 cm long, p = 10 • 12 = 120 cm. Use trigonometry to find a.

  2. Use the tangent ratio. 6 a tan 18° = 6 tan 18° a = Solve for a. Substitute for a and p. 1 2 A = ap Simplify. 360 18 Use a calculator. 6 . tan 18° 1 2 360 tan 18° A = • • 120 A = Trigonometry and Area LESSON 10-5 Additional Examples (continued) Now substitute into the area formula. The area is about 1108 cm2. Quick Check

  3. Find the perimeter p and apothem a, and then find the area using the formula A = ap. 1 2 360 5 Because the pentagon has 5 sides, mACB = = 72. CA and CB are radii, so CA = CB. Therefore, ACMBCM by the HL Theorem, so mACM = mACB = 36. 1 2 Trigonometry and Area LESSON 10-5 Additional Examples The radius of a garden in the shape of a regular pentagon is 18 feet. Find the area of the garden.

  4. Use the cosine ratio to find a. Use the sine ratio to find AM. AM 18 a 18 sin 36° = cos 36° = Use the ratio. a = 18(cos 36°) Solve. AM = 18(sin 36°) Use AM to find p. Because ACMBCM, AB = 2 • AM. Because the pentagon is regular, p = 5 • AB. Trigonometry and Area LESSON 10-5 Additional Examples (continued) So p = 5 • (2 • AM) = 10 • AM = 10 • 18(sin 36°) = 180(sin 36°).

  5. 1 2 A = • 18(cos 36°) • 180(sin 36°) Substitute for a and p. A = 1620(cos 36°) • (sin 36°) Simplify. Use a calculator. A Trigonometry and Area LESSON 10-5 Additional Examples (continued) 1 2 Finally, substitute into the area formula A = ap. The area of the garden is about 770 ft2. Quick Check

  6. A triangular park has two sides that measure 200 ft and 300 ft and form a 65° angle. Find the area of the park to the nearest hundred square feet. 1 2 Area = • side length • side length Theorem 10-8 • sine of included angle Substitute. 1 2 Area = • 200 • 300 • sin 65° Area = 30,000 sin 65° Simplify. Use a calculator Trigonometry and Area LESSON 10-5 Additional Examples Use Theorem 10-8: The area of a triangle is one half the product of the lengths of two sides and the sine of the included angle. Quick Check The area of the park is approximately 27,200 ft2.

More Related