. Elements of geometry : containing books I to III. Produce DC to F, making CF=AB. Join AF, cutting BC in 0. Then in As AOB, COF, :? lBA0= l CFO. and l A0B= l FOC, and AB=CF; .-. lC0F=aA0B. Hence trapezium ABCD = &ADF. Now suppose the measures of AB, CD, A IS to be m. n, prespectively . .. measure of DF=m + n, . CF=AB. Then measure oi area of trapezium measure of DF X measure of AE) =4 (< + »0 x P- That is, the measure of the area of a trapezium is fom (,,multiplying half the measure of the sum of the parallel aidesbv the measure of the perpendicular distance between theparallel sides
. Elements of geometry : containing books I to III. Produce DC to F, making CF=AB. Join AF, cutting BC in 0. Then in As AOB, COF, :? lBA0= l CFO. and l A0B= l FOC, and AB=CF; .-. lC0F=aA0B. Hence trapezium ABCD = &ADF. Now suppose the measures of AB, CD, A IS to be m. n, prespectively . .. measure of DF=m + n, . CF=AB. Then measure oi area of trapezium measure of DF X measure of AE) =4 (< + »0 x P- That is, the measure of the area of a trapezium is fom (,,multiplying half the measure of the sum of the parallel aidesbv the measure of the perpendicular distance between theparallel sides. EUCLIDS J: : Ml [Books I. & TI Area of an Irregular Polygon. There are three methods of finding the area of an irregularpolygon, which we shall here briefly notice. I. Tin polygon may be divided into triangles, and thearea of each of these triangles be found separately. Thus the area of the irregular polygon ABODE is equalto the sum of the areas of the triangles ABE, EBD, DBC. II. Tin polygon may be co verted into a single triaoj i qua! <• It ABODE be a pentagon, we can convert it into anequivalent quadrilateral by the following pro
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