Question 83

How many triangles are there in the figure given below?

image

Solution

Label the square ABCD with A top left, B top right, C bottom right and D bottom left, and centre O; the figure has both mid-lines, the full diagonal BD and the half diagonal AO. The small triangles are two in each of the three divided quadrants, giving 6. The larger triangles are ABO, AOD, ABD and BCD, giving 4 more. In all there are $$6 + 4 = 10$$ triangles.

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