9.12 2.2105 9.16 8.63 2.1552 9.13 2.2116 8.64 2.1564 9.14 2.2127 8.65 2.1576 9.15 2.2138 8.66, 2.1587 2.2148 8.67 2.1599 9.17 2.2159 8.68 2.1610 9.18 2.2170 8.69 2.1622 9.19 2.2181 8.70 2.1633 9.20 2.2192 8.71, 2.1645 9.21 2.2203 8.72 2.1656 9.22 2.2214 8.73 2.1668 9.23 2.2225 8.74 2.1679 9.24 2.2235 8.75 2.1691 9.25 2.2246 8.76 2.1702 9.26 2.2257 18.77 2.1713 9.27 2.2268 8.78 2.1725 9.28 2.2279 8.79 2.1736 9.29 2.2289 8.80 2.1748 9.30 2.2300 8.81 2.1759 9.31 2.2311 8.82 2.1770 9.32 2.2322 8.83 2.1782 9.33 2.2332 8.84 2.1793 9.34 2.2343 8.85 2.1804 9.35 2.2354 8.86 2.1815 9.36 2.2364 8.87 2.1827 9.37 2.2375 8.88 2.1838 9.38 2.2386 8.89 2.1849 9-39 2.2396 8.90 2.1861 9.40 2.2407 8.91 2.1872 9.41 2.2418 8.92 2.1883 9.42 2.2428 8.93 2.1894 9.43 2.2439 8.94 2.1905 9.44 2.2450 8.95, 2.1917 9.45 2.2460 8.96 2.1928 9.46 2.2471 8.97 2.1939 9.47 2.2481 9.97 2.2996 8.98 2.1950 9.48 2.2492 9.98 2.3006 8.99 2.1961 9.49 2.2502 9.99 2.3016 9.00 2.1972 9.50 2.2513 10.00 2.3026 9.73 2.2752 16.50 2.8034 9.62 2.2638 13.00 2.5649 52 3.9512 9.63 2.2649 9.64 2.2659 9.65 2.267013.75 2.6211 55 4.0073 9.66 2.2680 9.67 2.2690 9.68 2.2701 9.69 2.271I 14.75 2.6913 59 58 4.0775 4.0943 Mensuration In the following tables are given the areas of plane figures, together with other formulas relating to their dimensions and properties; the surfaces of solids; and the volumes of solids. The notation used in the formulas is, as far as possible, given in the illustration accompanying them; where this has not been possible, it is given at the beginning of each set of formulas. Examples of the Use of the Formulas Below are given a number of examples showing the use of the formulas on the opposite page. Each section of the page corresponds to the opposite section on the previous page, and the illustration on that page should be referred to notation used in the illustrations is also used in the examples given. Square. The Assume that the side s of a square is 15 inches. Find the area and the length of the diagonal. Area = A = s2 = 152 = 225 square inches. Diagonal = d = 1.414 S = 1.414 X 15 = 21.21 inches. The area of a square is 625 square inches. Find the length of the side s and the diagonal d. Rectangle. s = √A = √625 = 25 inches. The side a of a rectangle is 12 inches, and the area 70.5 square inches. Find the length of the side b, and the diagonal d. d b = A + a = 70.5 ÷ 12 = 5.875 inches. == √ a2 + b2 = √ 122 + 5.8752 = √178.516 = 13.361 inches. The sides of a rectangle are 30.5 and 11 inches long. Find the area. Parallelogram. The base b of a parallelogram is 16 feet. The height a is 5.5 feet. Find the area. Area = A = ax b = 5.5 × 16 = 88 square feet. The area of a parallelogram is 12 square inches. The height is 1.5 inch. Find the length of the base b. Right-angled Triangle. — The sides b and c in a right-angled triangle are 6 and 8 inches. Find side a and the area. a = √ b2 + c2 = √62 + 82 = √36 + 64 = √100 = 10 inches. If a 10 and b = 6, had been known, but not c, the latter would have been found as follows: c = √a2-b2 = √102 62 = √100 36 648 inches. Acute-angled Triangle. — If a = 10, b = 9, and c = 8 inches, what is the area of the triangle? = √ 5.5 × 0.5 × 1.5 X 3.5 = √14.437 = 3.8 square inches. Side a 23 feet, side b= 32 feet, and height h 12 feet. (a+b) h (23+32) 12 2 Regular Hexagon. — The side s of a regular hexagon is 4 inches. Find the area and the radius of the inscribed circle. A = 2.598 52 = 2.598 X 42 = 2.598 × 16 = 41.568 square inches. =0.866 s = 0.866 X 4 = 3.464 inches. What is the length of the side of a hexagon that is described about a circle of 5 inches radius? - Herer 5. Hence, S = 1.1557 = 1.155 X 5 = 5.775 inches. Regular Octagon. - Find the area and the length of the side of an octagon that is inscribed in a circle of 12 inches diameter. Diameter of circumscribed circle = 12 inches; hence, R = 6 inches. A 2.828 R2 = 2.828 X 6a = 2.828 X 36 = 101.81 square inches. Regular Polygon. - Find the area of a polygon having 12 sides, inscribed in a circle of 8 inches radius. The length of the side s is 4.141 inches. |