Problem 4 · 2012 Math Kangaroo
Easy
Geometry & Measurement
areaarea-decomposition
M and N are the midpoints of the equal sides of an isosceles triangle. How big is the area of the quadrilateral (marked ?)?
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Answer: D — 6
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Hint 1 of 2
The two segments are medians (they go to the midpoints of the equal sides).
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Hint 2 of 2
Two medians cut the triangle into six equal small triangles at the centroid.
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Approach: use that two medians split a triangle into six equal parts
- M and N are midpoints, so the drawn segments are medians; they meet at the centroid and divide the whole triangle into six equal small triangles.
- The bottom region is two of those small triangles and is marked 6, so each small triangle has area 3 (matching the two side regions marked 3).
- The quadrilateral marked ? is made of two small triangles as well, so its area is 3 + 3 = 6.
- The answer is 6 (D).
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