Examples for Practice. 4. If the two diagonals of a trapezium be 920 and 870, and the of intersection 89° 10', what is the area? Ansr. 400157.658. 5. The two perpendiculars falling on the diagonal of a trapezium are 650 and 810, and the diagonal itself 1140; what is the content? Ansr. 832200. 6. The four sides of a trapezium inscribed in a circle are 427, 517, 620, and 810 links; what is the area? Ansr. 329918.2 sq. links. 7. The diagonal of a trapezium is 1241, and sum of the perpendiculars 1527 links; what is the area? Ansr. 947503.5 8. What is the area of a trapezium, the side AB being =650, BC = 660, CD = 880, and AD = 915; and whose angle at A = 89°, and angle C = 93° ? Multiply half the sum of the parallel sides by the direct distance between them, and the product will be 1. Required the area of a trapezoid, the parallel sides of which are 1080 and 890, and which are distant from each other 610 links. 2. What is the area of a trapezoid, the parallel sides being 920 and 579, and whose direct distance one from another, is 607 links? Ansr. 454946.5 sq. links. 3. Required the area of a trapezoid, where the parallel sides are 340 and tance 486. 580 links, and direct disAnsr. 223560 sq. links. are contained in a trawhich are 140 and 270, Ansr. 65600 sq. links. 4. How many square links pezoid, the parallel sides of and distance 320 ? When a side and a perpendicular are given. Multiply half the perimeter of the polygon by * The perimeter is the sum total of the sides of any plane figure; and, in a regular polygon, is equal to one side multiplied by the number of sides The central angles of regular polygons are found by dividing 360° by the number of sides; the quotient shows the number of degrees comprehended in each portion of the polygon. These degrees being taken in the compasses from a sector or plain scale, and successively applied to the circumference of a circle, comprehending the polygon, will determine the points of the external angles of the polygon. The sides may also be set off with proportional compasses: by setting the sliding centre to the number of sides, on the scale marked circles, taking the radius of the surrounding circle in the longer points, and applying the shorter ends to the circumference, the sides of the polygon will be readily pointed off. the perpendicular demitted from its centre to one of the sides, and the product will be the area, Square a side of any regular polygon, and multiply the said square by the multiplier opposite the name of the polygon in the following table; and the product will be the area. That is, AB2 x tabular number = area. 1. What is the area of a hexagon, each side of which is 470, and perpendicular from the centre to a side 415? G 2. Required the area of a pentagon, each side being 25. By Rule II. 252 = 625. Tabular number 1.720477 × 625 = 1075.298, &c. Examples for Practice. 3. What is the area of a hexagon, the side being 466? Ansr. 564187.79. 4. Required the area of a pentagon, the side being 250 links. Ansr. 107529.81 links. 5. What is the area of a trigon, the side of which is 769? Ansr. 256067. 6. Required the area of a hexagon, the side of which is 850 links, and perpendicular 732. Ansr. 1866600 square links. CIRCLE. Hitherto I have been explaining the principles on which the areas of figures, bounded by straight lines, are founded; and these, it must be confessed, are the figures which mostly occur in the practice of landmeasuring but, as figures of other forms (particularly circular and elliptical) sometimes occur in practice, it is necessary to pay some attention to them also. |