2010 UNCO Math Contest II Problems/Problem 2

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

The shaded area is $\frac 25$ of the area of the rectangle, which is $\dfrac 25\cdot 75 \cdot 67 = \boxed {2010}.$

2010 UNCO Math Contest II (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10
All UNCO Math Contest Problems and Solutions

Page

Toolbox

Search

2010 UNCO Math Contest II Problems/Problem 2

Problem

Solution

See also