Ex. 509. Find the perimeter of a regular pentagon inscribed in a circle whose radius is 25 feet. Ex. 510. The length decagon is 100 yards. Now of each side of a park in the shape of a regular Find the area of the park. SrP = rx 10 a 5 ar. a = R(√5-1). § 459 Ex. 443 2 a (√5 + 1) = ƒ a (√5 + 1). r = √4 R2 a2 5-1 = + √ a2 (√5 + 1)2 — a2 ..S=5axa √5+2√5 = a2 × √5+2 × 2.23606 Ex. 506 Ex. 511. Find the cost, at $2 per yard, of building a wall around a cemetery, in the shape of a regular hexagon, that contains 16,627.84 square Ex. 512. The side of an inscribed regular polygon of n sides is 16 feet. Find the side of an inscribed regular polygon of 2 n sides. Ex. 513. If the radius of a circle is R, and the side of an inscribed regular polygon is a, show that the side of the similar circumscribed regular 2 aR polygon is Let AB, the side of a regular inscribed polygon, be denoted by a, and the radius of the by R. Let CD be a side of the similar circumscribed regular polygon. To prove that § 441 Ex. 514. What is the width of the circular ring between two concentric circumferences whose lengths are 650 feet and 425 feet? Let R be the radius of the larger O, and R' the radius of the smaller. Since § 458 С = 2 πR, Ex. 515. Find the angle subtended at the centre by an arc 5 feet 10 inches long, if the radius of the circle is 9 feet 4 inches. Ex. 516. The chord of a segment is 10 feet and the radius of the circle is 16 feet. Find the area of the segment. Δ ΟΑΒ. = = area sector OACB area Inscribe in a O whose radius is unity a sector O'A'C'B' similar to the sector OACB. D Then A'B': AB = O'B': OB. ... A'B': 10 = 1:16. ... A'B' = 18 = 0.625. = 0.625. The arc of the sector can be found approximately by a method similar to that used in § 480. No. of C1 = Sum of Chords. 0.625 Therefore, the length of the arc AB is 0.6358, correct to four places of decimals. = 0.3179. § 462 § 465 Area ▲ OAB = √s (s − a) (s — b) (s — c) Ex. 405 Ex. 517. Find the area of a sector, if the angle at the centre is 20°, and the radius of the circle is 20 inches. Ex. 518. is 18 feet. = The chord of half an arc is 12 feet, and the radius of the circle Ex. 519. Find the side of a square which is equivalent to a circle whose diameter is 35 feet. = Area R2 = ‡ πD2 = ‡ × 3.1416 × 352 = 962.115. § 463 31.02 ft. Ans. Ex. 520. The diameter of a circle is 15 feet. Find the diameter of a circle twice as large. Three times as large. Let S and D' denote the area and diameter of the required O. Ex. 521. Find the radii of the concentric circumferences that divide a circle 11 inches in diameter into five equivalent parts. Let S and R' denote the area and radius of the required O. Ex. 522. The perimeter of a regular hexagon is 840 feet, and that of a regular octagon is the same. By how many square feet is the octagon larger than the hexagon? of 840 ft. = 140 ft. 6 times the area of an equilateral ▲ of 140 ft. side. 1402 x √3 4 V 6 x 8487.045 sq. ft. = 50,922.270 sq. ft. = of 840 ft. = 105 ft. 4900 x 1.732058487.045. Ex. 404 53,228.700 sq. ft. - 50,922.270 sq. ft. = 2306.430 sq. ft. Ans. Ex. 523. The diameter of a bicycle wheel is 28 inches. revolutions does the wheel make in going 10 miles? How many = 52,800 ft. = = 7.3304 ft. § 458 7.3304 = 7202 +. |