DIMENSIONS OF PLANE FIGURES Machinery's Handbook, 31st Edition
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Dimensions of Plane Figures The following pages contain diagrams of plane figures, along with formulas for finding their dimensions. Illustrations are labeled with the variables given in the formulas. For- mulas for one dimension are derived from another by rearranging terms or substituting the formula for one dimension with another, where appropriate. Formulas that include decimals are derived either from the square root of 2 or 1 ⁄ 2 . As such, they are approximations of the dimension being solved for. Formulas that include π are approximated as well. The dimensions generally are as follows, with distinctions shown as needed for each figure: A = area; s = side; d = diagonal or diameter; h, H = height; a, b, c = sides or other segments as shown; r, R = radius; l = arc length or other. Square: = = s 0.7071 d A = = d 1.414 s 1.414 A = = Example: Side s of a square is 15 in. Find the area of the square and the length of its diagonal. A s 2 15 2 225 = = = d 1.414 s 1.414 15 × 21.21 = = = in 2 in Example: The area of a square is 625 cm 2 . Find the length of side s and diagonal d . s A 625 25 cm = = = d 1.414 A 1.414 25 × 35.35 cm = = = Rectangle: s s d A s 2 1 ⁄ 2 d 2
A ab a d 2 a 2 – b d 2 b 2 – = = = d a 2 b 2 = +
a
d
b / / Example: Side a of a rectangle is 12 cm, and the area is 70.5 cm 2 . Find the length of side b and diagonal d . b A a / 70.5 12 / 5.875 = = = d a 2 b 2 + 12 2 5.875 2 + 178.516 13.361 = = = = cm cm Example: The sides of a rectangle are 30.5 and 11 cm. Find the area. A ab 30.5 11 × 335.5 cm 2 = = = Parallelogram: a d 2 b 2 – A b = = b d 2 a 2 – A a = =
A ab = a A b = b A a = / /
a
Note: The dimension a is the length of the vertical drawn at a right angle to side b . Dimension a is also considered the height of the parallelogram.
b
Example: Base b of a parallelogram is 16 ft. Height a is 5.5 ft. Find the area. A ab 5.5 16 × 88 ft 2 = = = Example: The area of a parallelogram is 12 in 2 . The height is 1.5 in. Find the length of the base b . b A a 12 1.5 8in. = = = / /
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