. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. wo opposite angles ; then add these two perpendiculars together,and multiply that sum by the diagonal, taking half the product forthe area of the trapezium. Ex. 1. To find the area of the trapezium, whose diagonal is 42,and the two perpendiculars on it 16 and 16+18= 34, its half is 42 X 17= 714 the area. Ex. 2. How many square yards of paving are in the trapezium,whose diagonal is 65 feet; and the two perpendiculars let fall on it28 and 33| feet ? An
. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. wo opposite angles ; then add these two perpendiculars together,and multiply that sum by the diagonal, taking half the product forthe area of the trapezium. Ex. 1. To find the area of the trapezium, whose diagonal is 42,and the two perpendiculars on it 16 and 16+18= 34, its half is 42 X 17= 714 the area. Ex. 2. How many square yards of paving are in the trapezium,whose diagonal is 65 feet; and the two perpendiculars let fall on it28 and 33| feet ? Ans. 222-^ yards. When the sides of a trapezium, and two of its opposite angles aregiven, the most convenient rule for finding its area is found inproblem III. Conceive CB joined, then the whole figureconsists of two triangles and the whole areais found in the following expression(AB X ACX ) + (CD X DB X ) EXAMPLE. In the quadrilateral A CDB we have AC , CD , , and BA rods. The angle A 78° 15 and the oppositeangle CDB 97° 30. What is the area enclosed ? Ans. square rods. PROBLEM To find the area of an irregular figure bounded by any numberof right lines. Rule. — Draw diagonals dividing the figure into triangles. Findthe areas of the triangles so formed and add them together for the areaof the whole. Let it be required to find thearea of the adjoining figure offive sides. On the suppositionthat AC= .#(7= Bb=4 and Dd=
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