WarmUp Exercises 1 An isosceles triangle has side

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Warm-Up Exercises 1. An isosceles triangle has side lengths 20 meters, 26 meters, and

Warm-Up Exercises 1. An isosceles triangle has side lengths 20 meters, 26 meters, and 26 meters. Find the length of the altitude to the base. ANSWER 24 m 2. Solve 18 = 21 ANSWER 36 x.

Warm-Up Exercises 3. Evaluate (4 cos 10º)(10 sin 20º). ANSWER 4. Evaluate ANSWER 13.

Warm-Up Exercises 3. Evaluate (4 cos 10º)(10 sin 20º). ANSWER 4. Evaluate ANSWER 13. 47 10. tan 88º 0. 3492

Find angle measures in a regular polygon Warm-Up 1 Exercises EXAMPLE In the diagram,

Find angle measures in a regular polygon Warm-Up 1 Exercises EXAMPLE In the diagram, ABCDE is a regular pentagon inscribed in F. Find each angle measure. a. m AFB SOLUTION AFB is a central angle, so m 72°. ° 360 AFB = , or 5

Find angle measures in a regular polygon Warm-Up 1 Exercises EXAMPLE In the diagram,

Find angle measures in a regular polygon Warm-Up 1 Exercises EXAMPLE In the diagram, ABCDE is a regular pentagon inscribed in F. Find each angle measure. b. m AFG SOLUTION FG is an apothem, which makes it an altitude of isosceles ∆AFB. So, FG bisects AFB and m 1 AFB = 36°. AFG = m 2

Find angle measures in a regular polygon Warm-Up 1 Exercises EXAMPLE In the diagram,

Find angle measures in a regular polygon Warm-Up 1 Exercises EXAMPLE In the diagram, ABCDE is a regular pentagon inscribed in F. Find each angle measure. c. m GAF SOLUTION The sum of the measures of right ∆GAF is 180°. So, 90° + 36° + m GAF = 180°, and m GAF = 54°.

Warm-Up Exercises GUIDED PRACTICE for Example 1 In the diagram, WXYZ is a square

Warm-Up Exercises GUIDED PRACTICE for Example 1 In the diagram, WXYZ is a square inscribed in 1. Identify the center, a radius, an apothem, and a central angle of the polygon. ANSWER P, PY or XP, PQ, XPY. P.

Warm-Up Exercises GUIDED PRACTICE 2. Find m ANSWER 90°, 45° XPY, m for Example

Warm-Up Exercises GUIDED PRACTICE 2. Find m ANSWER 90°, 45° XPY, m for Example 1 XPQ, and m PXQ.

Find the area of a regular polygon Warm-Up 2 Exercises EXAMPLE DECORATING You are

Find the area of a regular polygon Warm-Up 2 Exercises EXAMPLE DECORATING 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? SOLUTION STEP 1 Find the perimeter P of the table top. An octagon has 8 sides, so P = 8(15) = 120 inches.

Find the area of a regular polygon Warm-Up 2 Exercises EXAMPLE STEP 2 Find

Find the area of a regular polygon Warm-Up 2 Exercises EXAMPLE STEP 2 Find the apothem a. The apothem is height RS of ∆PQR. Because ∆PQR is isosceles, altitude RS bisects QP. So, QS = 1 (QP) = 1 (15) = 7. 5 inches. 2 2 To find RS, use the Pythagorean Theorem for ∆ RQS. a = RS ≈ √ 19. 62 – 7. 52 = √ 327. 91 ≈ 18. 108

Find the area of a regular polygon Warm-Up 2 Exercises EXAMPLE STEP 3 Find

Find the area of a regular polygon Warm-Up 2 Exercises EXAMPLE STEP 3 Find the area A of the table top. 1 Formula for area of regular polygon A = 2 a. P 1 ≈ (18. 108)(120) 2 Substitute. ≈ 1086. 5 Simplify. ANSWER So, the area you are covering with tiles is about 1086. 5 square inches.

Find the perimeter and area of a regular polygon Warm-Up 3 Exercises EXAMPLE A

Find the perimeter and area of a regular polygon Warm-Up 3 Exercises EXAMPLE 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 JLK is 9 , or 40°. Apothem LM bisects the central angle, so m KLM is 20°. To find the lengths of the legs, use trigonometric ratios for right ∆ KLM.

Find the perimeter and area of a regular polygon Warm-Up 3 Exercises EXAMPLE 4

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

Find the perimeter and area of a regular polygon Warm-Up 3 Exercises EXAMPLE ANSWER

Find the perimeter and area of a regular polygon Warm-Up 3 Exercises EXAMPLE ANSWER So, the perimeter is P = 9 s = 9(8 sin 20°) = 72 sin 20° ≈ 24. 6 units, 1 1 and the area is A = a. P = (4 cos 20°)(72 sin 20°) 2 2 ≈ 46. 3 square units.

Warm-Up Exercises GUIDED PRACTICE for Examples 2 and 3 Find the perimeter and the

Warm-Up Exercises GUIDED PRACTICE for Examples 2 and 3 Find the perimeter and the area of the regular polygon. 3. ANSWER about 46. 6 units, about 151. 5 units 2

Warm-Up Exercises GUIDED PRACTICE for Examples 2 and 3 Find the perimeter and the

Warm-Up Exercises GUIDED PRACTICE for Examples 2 and 3 Find the perimeter and the area of the regular polygon. 4. ANSWER 70 units, about 377. 0 units 2

Warm-Up Exercises GUIDED PRACTICE for Examples 2 and 3 Find the perimeter and the

Warm-Up Exercises GUIDED PRACTICE for Examples 2 and 3 Find the perimeter and the area of the regular polygon. 5. ANSWER 30 3 52. 0 units, about 129. 9 units 2

Warm-Up Exercises GUIDED PRACTICE 6. for Examples 2 and 3 Which of Exercises 3–

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

Warm-Up Exercises Daily Homework Quiz 1. Find the measure of the central angle of

Warm-Up Exercises Daily Homework Quiz 1. Find the measure of the central angle of a regular polygon with 24 sides. ANSWER 15° Find the area of each regular polygon. 2. ANSWER 110 cm 2

Warm-Up Exercises Daily Homework Quiz 3. ANSWER 374. 1 cm 2

Warm-Up Exercises Daily Homework Quiz 3. ANSWER 374. 1 cm 2

Warm-Up Exercises Daily Homework Quiz Find the perimeter and area of each regular polygon.

Warm-Up Exercises Daily Homework Quiz Find the perimeter and area of each regular polygon. 4. ANSWER 99. 4 in. ; 745. 6 in. 2

Warm-Up Exercises Daily Homework Quiz 5. ANSWER 22. 6 m; 32 m 2

Warm-Up Exercises Daily Homework Quiz 5. ANSWER 22. 6 m; 32 m 2

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