2010 UNCO Math Contest II Problems/Problem 2

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Problem

The rectangle has dimensions $67 \times 75$. The diagonal $AB$ is divided into five segments of equal length. Find the total area of the shaded regions.

[asy] pair A,B,C,D; A==(0,0);B=(75,0);C=(75,67);D=(0,67); draw(A--B--C--D--cycle,black); filldraw(A--(D+.2(B-D))--C--(D+.4(B-D))--cycle,blue); filldraw(A--(D+.6(B-D))--C--(D+.8(B-D))--cycle,blue); draw(B--D,black); dot(D+.2(B-D));dot(D+.4(B-D));dot(D+.6(B-D));dot(D+.8(B-D)); MP("A",D,NW);MP("B",B,SE); [/asy]


Solution

Notice the rectangle is divided into 10 triangles of equal triangles. Therefore, the shaded area is $\frac 25$ of the area of the rectangle, which is $\dfrac 25\cdot 75 \cdot 67 = \boxed {2010}.$

See also

2010 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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All UNCO Math Contest Problems and Solutions
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