. Elements of geometry : containing books I to III. It 18 easy to prove that .I and Bl> bisbct each other atright angles. Tlieii if the measure of AC be 35,and ..., /./ ... /. measure of ar a of rhombus=tw ice measure of &ACD. ?» twice I- •?./ Books I. & II] A ALA Ul- A TRAPEZIUM. 99 Area oj a Trap :;um. Let ABCD be the given trapezium, having the Bides AB,CD parallel. Draw AE at right angles to 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 meas
. Elements of geometry : containing books I to III. It 18 easy to prove that .I and Bl> bisbct each other atright angles. Tlieii if the measure of AC be 35,and ..., /./ ... /. measure of ar a of rhombus=tw ice measure of &ACD. ?» twice I- •?./ Books I. & II] A ALA Ul- A TRAPEZIUM. 99 Area oj a Trap :;um. Let ABCD be the given trapezium, having the Bides AB,CD parallel. Draw AE at right angles to 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. r.
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