Math CentralQuandaries & Queries


Question from Cathy, a student:

An octagonal sign is made by cutting four identical triangles made from a rectangle calculate area of one of the discarded triangles.length of square=26cmx22cm.length of octagonal sides are 10cm x 13cm

Hi Cathy,

I drew the diagram that came to my mind when I read your question.

Each of the identical yellow triangles you remove is a right triangle. What are the lengths of the legs of the triangles? What are their areas?

There is another answer to this question. You could form the 10 cm side of the octagon from the 26 cm side of the rectangle and the 13 cm side of the octagon from the 22 cm side of the rectangle. If you do this the dimensions of the triangles you discard are different that they were in my diagram. What are the areas of the triangles in this situation?

I hope this helps,

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