Question

find area of a quadrilateral ABCD in which AB=3 cm,BC=4cm,CD=4cm ,DA=5cm and AC=5cm (chapter herons formula maths m.l aggarwal)

Answer 1

First we draw AE perpendicular to DC. So we get a triangle AEC. In AEC we know AC = 5 cm. EC = AB as ABEC ia a rectangle. So EC = 3 cm. In ∆AEC AC=hypotenuse EC=base AE=perpendicular. By following Pythagoras Theorem we get AE=4. Then applying the area formula of a trapezium i.e 1\2 × sum of parallel sides ×height =1\2×(3+4) ×4 we get 14 as the answer. Thus area of trapezium ABCD= 14 sq.cm