_To find the area of a rectangle._ Multiply together the units in two sides which meet, or multiply together two sides which meet; the product is the number of square units in the area. Thus, if 6 feet and 5 feet be the sides, the area is 6 × 5, or 30 square feet. Similarly, the area of a square of 6 feet long is 6 × 6, or 36 square feet (234). _To find the area of a parallelogram._ Multiply one side by the perpendicular distance between it and the opposite side; the product is the area required in square units. _To find the area of a trapezium._[77] Multiply either of the two sides which are not parallel by the perpendicular let fall upon it from the middle point of the other. [77] A four-sided figure, which has two sides parallel, and two sides not parallel. _To find the area of a triangle._ Multiply any side by the perpendicular let fall upon it from the opposite vertex, and take half the product. Or, halve the sum of the three sides, subtract the three sides severally from this half sum, multiply the four results together, and find the square root of the product. The result is the number of square units in the area; and twice this, divided by either side, is the perpendicular distance of that side from its opposite vertex. _To find the radius of the internal circle which touches the three sides of a triangle._ Divide the area, found in the last paragraph, by half the sum of the sides. _Given the two sides of a right-angled triangle, to find the hypothenuse._ Add the squares of the sides, and extract the square root of the sum. _Given the hypothenuse and one of the sides, to find the other side._ Multiply the sum of the given lines by their difference, and extract the square root of the product. _To find the circumference of a circle from its radius, very nearly._ Multiply twice the radius, or the diameter, by 3·1415927, taking as many decimal places as may be thought necessary. For a rough computation, multiply by 22 and divide by 7. For a very exact computation, in which decimals shall be avoided, multiply by 355 and divide by 113. See (131), last example. _To find the arc of a circular sector, very nearly, knowing the radius and the angle._ Turn the angle into seconds,[78] multiply by the radius, and divide the product by 206265. The result will be the number of units in the arc. [78] The right angle is divided into 90 equal parts called _degrees_, each degree into 60 equal parts called _minutes_, and each minute into 60 equal parts called _seconds_. Thus, 2° 15′ 40″ means 2 degrees, 15 minutes, and 40 seconds. _To find the area of a circle from its radius, very nearly._ Multiply the square of the radius by 3·1415927. _To find the area of a sector, very nearly, knowing the radius and the angle._ Turn the angle into seconds, multiply by the square of the radius, and divide by 206265 × 2, or 412530.