mid-points of the sides of a 4-gon – Discussion Forum

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Kriti

Asked: September 17, 2026In: Class 9 Maths

If the mid-points of the sides of a 4-gon (also known as a quadrilateral, but we prefer to call it a ‘4-gon’) are joined in order, prove that the area of the parallelogram thus formed will be half of the area of the given 4-gon. (You may wonder whether the 4-gon thus formed is always a parallelogram and if so, why? These questions will be tackled and answered in the chapter on quadrilaterals.)

Midpoints cut each corner triangle’s area to 1/4 of its diagonal triangle. Summing opposite corner triangles removes 1/4 + 1/4 = 1/2 of the total 4-gon area, leaving exactly half for the inner Varignon parallelogram.