Category: Geometry

How to transform a pentagon into a triangle of the same area

This is the third in the series of problems involving transforming polygons into another polygon where the area is preserved. The first is about transforming a shape into another shape of the same area and the second is about transforming a quadrilateral into a triangle of the same area. The following problem builds on the…

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How to transform quadrilaterals into triangles with the same area

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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Transforming shapes without changing their areas

Under any of Euclidean transformations—reflection, rotation, and translation, the shape of a geometric object will not change; only the position and orientation of the object will change. That is, the object and its transformation are congruent. How about when the shape can change but the area remain unchanged? Try this problem.   Problem How do you…

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How many squares do you see?

If you enjoyed the Facebook math problem about PEMDAS, I’m sure you will love this second math problem about counting squares which I also got from Facebook. Problem How many squares do you see? Answers given in Facebook include 24, 25, 26, 27, 38, 34, 36, 40, 42. Solution Here’s how you can systematically count the…

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