AREAS OF PARALLELOGRAMS AND TRIANGLES

Question

1. AB and CD are parallel sides of trapezium ABCD. Diagonals AC and BD intersect at O. prove that ar(ΔAOD) = ar(ΔBOC).

Answer 1

Draw and label a diagram!

area ΔACD =  area ΔBDC     equal base/height

area ΔACD = area ΔAOD + area ΔDOC

area ΔBDC = area ΔBOC + area Δ CO

area ΔAOD + area ΔDOC = area ΔBOC + area Δ COD

area ΔAOD = area ΔBOC