This section is from the book "Scientific American Reference Book. A Manual for the Office, Household and Shop", by Albert A. Hopkins, A. Russell Bond. Also available from Amazon: Scientific American Reference Book.
Area equals base multiplied by height.
Base and height given. Multiply base by height and divide by two.
When three sides are given. From the half sum of the three sides subtract each side separately; multiply the half sum and the three remainders together. The area is the square root of the product thus obtained.
To find the area multiply the sum of the two parallel sides by the distance between them and divide by two.
(an oblique parallelogram with four equal sides). - Area equals half the product of the diagonals.
The area may be found by dividing it into a series of triangles and trapeziums, and finding the sum of the areas thus obtained.
Area equals number of sides multiplied by length of one side and by the radius of the inscribed circle divided by two.
Circumference equals diameter multiplied by 3.1416, or approximately by 3 1/7. Area equals diameter squared multiplied by .7854.
Multiply the length of the arc by the radius and divide by two.
Find the area of the sector having the same arc. Also find area of triangle formed by the radial sides and the chord. The area equals the sum or difference of these according as the segment is greater or less than a semicircle.
Multiply the sum of the diameters by their difference and by .7854.
Side of square equals diameter multiplied by .8862.
Side of square equals diameter multiplied by .7071.
Area equals the product of the two axes by .7854.
Surface equals length of one edge squared and multiplied by six. Contents equals length of one edge cubed.
Surface equals perimeter of one end multiplied by height plus twice the area of one end. Contents equals area of base multiplied by height. This last also applies to oblique cylinders and prisms.
Surface equals circumference of base multiplied by slant height divided by two, plus the area of the base. Contents equals area of base multiplied by one-third perpendicular height. This last applies whether the cones and pyramids be right or oblique.
Contents : To the sum of the area of the two ends add the square root of their product and multiply the quantity thus obtained by one-third the perpendicular height.
Area equals square of diameter multiplied by 3.1416 or 3 1/7; i.e., it is equal to four times the area of one of its great circles, or to the convex surface of its circumscribing cylinder. Surfaces of spheres vary as the squares of their diameters. Contents equal the cube of the diameter multiplied by .5236, i.e., equals area of surface multiplied by diameter and divided by six. Contents of spheres vary as the cubes of the diameter.
Contents: From three times the diameter of the sphere subtract twice the height of the segment, multiply the difference by the square of the height and by .5236; or, another rule: Add -the square of the height to three times the square of the radius of the base and multiply the sum by the height and by .5236.
To the sum of the squares of the radii of the two ends add one-third the square of the height, multiply the sum by the height and by 1.5708.
The contents of a cone, sphere, and cylinder of same diameter and height are in the ratio of 1 to 2 to 3. - Practical Engineer's Electrical Pocket Book and Diary.