2. In Rectangles.—Divide the content by the length or breadth, according to which factor is known, and the result will be the required side.
Thus 5 acres, or 50 square chains, if 10 chains long, will require to be 5 chains wide.
If the content only is given, and the length is to be a certain number of times the breadth, the content in square chains divided by the ratio of the length to the breadth, and the square root of the quotient, will give the length of the shorter side. Thus, if we wish to lay out 72 acres as a rectangle twice as long as broad: 72 acres = 720 square chains, divided by 2, the ratio given, = 360, the square root of which is 18·97 chains, the length of the shorter side. The length of the other side is therefore 18·97 × 2 = 37·94 chains, or 3794 links.
MENSURATION.
To find the area of a triangle when the base and perpendicular height are given: Multiply the base by half the height, or vice versâ.
To find the area of a triangle when the three sides are given: Take half the sum of the sides, subtract each severally from this sum, then multiply this and the three remainders together, and take the square root for the area.
To find the area of a rectangular figure: Multiply the length by the breadth, the product will be the area.
To find the area of a trapezoid: Multiply half the sum of the two parallel sides by the distance between them.
To find the area of a parallelogram whose angles are not right angles: Multiply the length of any one of the sides by the perpendicular.