1 / 10

EXAMPLE 2

You are decorating the top of a table by covering it with small ceramic tiles. The table top is a regular octagon with 15 inch sides and a radius of about 19.6 inches . What is the area you are covering?. Find the area of a regular polygon. EXAMPLE 2. DECORATING. SOLUTION. STEP 1.

malo
Download Presentation

EXAMPLE 2

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. You are decorating the top of a table by covering it with small ceramic tiles. The table top is a regular octagon with 15inch sides and a radius of about 19.6inches. What is the area you are covering? Find the area of a regular polygon EXAMPLE 2 DECORATING SOLUTION STEP 1 Find the perimeter Pof the table top. An octagon has 8 sides, so P = 8(15) = 120inches.

  2. Find the apothem a. The apothem is height RSof ∆PQR. Because ∆PQRis isosceles, altitude RSbisects QP. 1 1 So,QS = (QP) = (15) = 7.5 inches. 2 2 √ a = RS ≈ √19.62 – 7.52 = 327.91 ≈ 18.108 Find the area of a regular polygon EXAMPLE 2 STEP 2 To find RS, use the Pythagorean Theorem for ∆ RQS.

  3. 1 A = aP 2 1 ≈ (18.108)(120) 2 ANSWER So, the area you are covering with tiles is about 1086.5square inches. Find the area of a regular polygon EXAMPLE 2 STEP 3 Find the area Aof the table top. Formula for area of regular polygon Substitute. ≈ 1086.5 Simplify.

  4. A regular nonagon is inscribed in a circle with radius 4 units. Find the perimeter and area of the nonagon. SOLUTION 360° The measure of central JLKis , or 40°. Apothem LMbisects the central angle, so m KLMis 20°. To find the lengths of the legs, use trigonometric ratios for right ∆KLM. 9 Find the perimeter and area of a regular polygon EXAMPLE 3

  5. LM MK sin 20° = cos 20° = LK LK MK LM cos 20° = sin 20° = 4 4 4 sin 20° = MK 4 cos 20° = LM The regular nonagon has side length s = 2MK = 2(4 sin 20°) = 8  sin 20° and apothem a = LM = 4  cos20°. Find the perimeter and area of a regular polygon EXAMPLE 3

  6. ANSWER So, the perimeter is P = 9s = 9(8 sin 20°) = 72 sin 20° ≈ 24.6 units, and the area is A = aP = (4 cos 20°)(72 sin20°)≈46.3 square units. 1 1 2 2 Find the perimeter and area of a regular polygon EXAMPLE 3

  7. 3. ANSWER about 46.6 units, about 151.5 units2 for Examples 2 and 3 GUIDED PRACTICE Find the perimeter and the area of the regular polygon.

  8. 4. ANSWER 70 units, about 377.0 units2 for Examples 2 and 3 GUIDED PRACTICE Find the perimeter and the area of the regular polygon.

  9. 5. 30 3  52.0units, about 129.9 units2 ANSWER for Examples 2 and 3 GUIDED PRACTICE Find the perimeter and the area of the regular polygon.

  10. ANSWER Exercise 5 for Examples 2 and 3 GUIDED PRACTICE 6. Which of Exercises 3–5 above can be solved using special right triangles?

More Related