Problem 18 · 2018 Math Kangaroo
Medium
Geometry & Measurement
area-decomposition
The diagram shows a rectangle and a straight line x, which is parallel to one of the sides of the rectangle. There are two points A and B on x inside the rectangle. The sum of the areas of the two triangles shaded in grey is 10 cm². How big is the area of the rectangle?
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Answer: B — 20 cm²
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Hint 1 of 2
Each grey triangle has the full width of the rectangle as its base and its apex on line x.
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Hint 2 of 2
Together the two triangles' heights add up to the height of the rectangle.
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Approach: add the two triangle areas using a common base
- Both triangles share the rectangle's width as base; one reaches up to the top side, the other down to the bottom side.
- Their heights sum to the rectangle's height, so together they cover ½ of the rectangle.
- Since that half is 10 cm², the rectangle is 20 cm².
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