If the polygon be regular, draw lines from the centre to two of the neighbouring angles, find the contents of the triangle thus formed, and multiply by the number of sides, which being all of a size, wifl make triangles of the same size.
4. A hexagonal basin has equal sides of 3,34 inches each. Its width from the centre of one side to the centre of the opposite side, is 4,88 inches. As half of this line drawn from side to side is the height of one of the triangles, the height is, 2,44 inches. Multiply the base, which in this case is the side, by half the height, and you have the answer. Ans. 24,42 square inches.
Problem IV. To find the surface of a trapezoid. (fig. 3.)
Rule. Take half the sum of the two parallel sides, and multiply by the height.
Example 1. A roof in the form of a trapezoid, has one of its parallel sides 44,7 feet, and the other 38,5 feet in length, and the height is 9,4 feet, what is the superficies ? Ans. 367,54 feet.
2. How many slates 15 inches long, and 12 wide, will cover the above roof ? Ans. 294.
Note. No allowance is here made for one slate's projecting over another, &c. This would only increase the size of the roof, but not alter the mode of calcula- tion. Change the feet of the roof into inches ; find the square inches in each slate, and divide the number of inches in the roof by the number in a slate.
Problem V. To find the surface, or superficial eon- tents of a circle.
Rule. Multiply the radius by itself, and then the product by 3^ (or 3,143.)
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