. Carpenter . by two. From this half-sum subtracteach side separately then multiply thesethree remainders and the half-sum togetherand extract the square root of their prod-uct. Wonderfully simple, isnt it? I told youthat you would have use for that squareroot rule. Let us see: 20 plus 16 plus 12 equals 48. 48 divided by 2 equals 24. Subtracting each side from 24 leaves4, 8 and 12. 4x8x12x24 equals 9216. Extracting the square root, we get 96square feet as the area. Try these different methods for findingthe area of an equilateral triangle, meas-uring 12 feet on each side. Then comparethe resul
. Carpenter . by two. From this half-sum subtracteach side separately then multiply thesethree remainders and the half-sum togetherand extract the square root of their prod-uct. Wonderfully simple, isnt it? I told youthat you would have use for that squareroot rule. Let us see: 20 plus 16 plus 12 equals 48. 48 divided by 2 equals 24. Subtracting each side from 24 leaves4, 8 and 12. 4x8x12x24 equals 9216. Extracting the square root, we get 96square feet as the area. Try these different methods for findingthe area of an equilateral triangle, meas-uring 12 feet on each side. Then comparethe results by that obtained when usingthe first of the following rules: The area of any regular polygon may befound by multiplying the square of oneside by a constant multiplier as Triangle Pentagon Hexagon Octagon Another method for finding the area ofpolygons is to divide them into as manytriangles as there are sides and find thearea of these triangles. Let us look at an octagon. (Fig. 3.) We. find a square with the corners cut off. Thefigure is supposed to measure 12 feet be-tween its parallel sides and the sides of theoctagon represent practically 5 feet. This proportion holds true for all octa-gons. Our multiplier above, times 25 (thesquare of a side) gives us feet area. Dividing it into triangles, we have 5x6x8divided by 2 equals 120 feet. Another method would be to computethe area of the corners removed, which, ifplaced together, would make a square a lit-tle less than 5 feet on a side. The original 24 from this gives 120 feet. A still more simple rule would be to 44 square the distance between the parallelsides and subtract one-sixth of it. 12x12 equals 144. 144 divided by 6 equals 24. 144^24 equals 120. In other words, to make a square intoan octagon we remove practically one-sixth of it. To make a square into a circle we re-move nearly one-fourth of it so that wehave .7854 of it left. That is a squaremeasuring 10 feet each way would contain
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