ABCD is a square and G is a point on its diagonal. Obviously, the two colored rectangles have equal area: ab. What about in the figure below? Problem: ACDB is a rectangle. E is a point on the diagonal. Which rectangle has a bigger area? GEIA or FEHD? Answer The diagonal divides a rectangle…

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Problem 1 Show that the area of a trapezoid (trapezium) is half its height times the sum of the parallel sides. Solution Cut the trapezoid along the midpoints of the pair of non-parallel side. This halves its height. Rotate one of the parts 180 degrees about a midpoint. In the figure below, it’s about the…

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Quadrilaterals have four sides. To make triangles out of them, three of the vertices should be collinear. Now, what construction should you make so that the area remain unchanged? Here’s how you can transform quadrilaterals into triangles with the same are in three easy steps. 1. Extend one of the sides of the quadrilateral. Let’s…

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