2020 · Q68
ABCD is a plate in the shape of a parallelogram. EF is the line parallel to DA and passing through the point of intersection O of the diagonals AC and BD. Further, E lies on DC and F lies on AB. The triangular portion DOE is cut out from the plate ABCD. What is the ratio of area of remaining portion of the plate to the whole?
Elementary MathematicsQuadrilaterals and Polygons
- A5/8
- B5/7
- C3/4
- D7/8
Explanation
Put D = (0, 0), C = (w, 0), A = (0, h), B = (w, h); area ratios are affine-invariant. The centre is O = (w/2, h/2) and EF ∥ DA gives E = (w/2, 0). △DOE has base DE = w/2 and height h/2, area wh/8 — one-eighth of the plate. The remaining area is 7/8 of the whole.