Draw the diagonal A C, upon which let fall from its opposite angles B, and D, the perpendiculars B F, D E. Find by measurement the diagonal A C, and the perpendiculars B F, D E, then multiply the sum of the perpendiculars by the diagonal, and half the product will be the area of the trapezium. [Fig. 18.]
Example.—Required the area of the trapezium, whose diagonal A C is 100 feet, and perpendiculars B F 30 feet, and D E 40 feet.
(30 + 40) × 100 2 = 3500 square feet. Area required.
Or, divide the trapezium into two triangles by a diagonal, then find the areas of these triangles, and add them together.
To find the area of a trapezoid, A B C D.
Multiply the sum of the parallel sides A B, D C by the perpendicular distance E C, and half the product will be the area. [Fig. 19.]
Example.—Required the area of the trapezoid A B C D, of which the parallel sides A B, D C are 120 feet, and 90 feet, and the perpendicular distance E C 40 feet.
(120 + 90) × 40 2 = 4200 square feet. Area required.
To find the area of an irregular figure, or polygon.
Draw diagonals dividing the figure into trapeziums, and triangles; then, having found the area of each, add them together, and the sum will be the area required.