Area Problem #34

What fraction is shaded?

shaded

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5 thoughts on “Area Problem #34

  1. 3/8 – The hexagon is composed of 6 equilateral triangles with sides of 1. The bottom of the shaded area is an equilateral triangle with side length of 1. Each equilateral triangle with side length 1 can be divided into 4 equilateral triangles of side length 1/2. The shaded area, above the portion composed of the equilateral triangle with sides of 1, is composed of 5 equilateral triangles with sides of 1/2. So, the total shaded area is composed of 9 triangles with side length of 1/2. The hexagon is composed of 6 equilateral triangles with sides of 1 which can each be decomposed into 4 equilateral triangles with sides of 1/2. So the hexagon is composed of 6*4 equilateral triangles of sides length 1/2. So the shaded area over the hexagon area = 9 equilateral triangles with sides of length 1/2 over 24 equilateral triangles with side length 1/2 = 9/24 = 3/8.

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