The Total Area ( 3 )

Geometry Level 2

What is the total area in blue knowing that the area of the large triangle is 1 1 ?

Image credit and problem source : wolfram

1 2 \frac{1}{2} 1 8 \frac{1}{8} 1 3 \frac{1}{3} 1 6 \frac{1}{6} 3 4 \frac{3}{4}

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

David Vreken
May 15, 2020

This pattern (not including the gray areas) is infinitely repeated in the diagram:

and since it is 9 9 parts blue congruent triangles to 12 12 parts total congruent triangles, the total area is A = 9 12 ⋅ 1 = 3 4 A = \frac{9}{12} \cdot 1 = \boxed{\frac{3}{4}} .

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