Problem 1 · 2013 Math Kangaroo
Easy
Geometry & Measurement
area-fractionarea-decomposition
Triangle ABC is equilateral and has area 9. The dividing lines are parallel to the sides and split each side into three equal lengths. What is the area of the grey shaded part of the triangle?
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Answer: D — 6
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Hint 1 of 2
The dividing lines split the equilateral triangle into nine little congruent triangles.
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Hint 2 of 2
Each little triangle has the same area, so just count how many of the nine are shaded.
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Approach: count congruent unit triangles
- Parallel lines cutting each side into three equal parts split the big triangle into 9 small congruent triangles.
- Since the whole area is 9, each small triangle has area 1.
- Counting the grey small triangles gives 6 of them.
- So the shaded area is 6.
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