Geoboard Triangle

The horizontal and vertical distances between adjacent points equal 1 unit. Find the area of triangle ABC.

Source: Julia Robinson Mathematics Festival

SOLUTION

area of triangle AEC = area of triangle ABC + area of triangle ADB + area of trapezoid BDCE
\frac{1}{2}AE\times EC = area of triangle ABC+ \frac{1}{2}AD\times DB+\frac{1}{2}DE\left (DB+EC\right )
Multiply both sides by 2
AE\times EC=2\times area of triangle ABC+ AD\times DB+DE\left (DB+EC\right )
4\times 3 = 2\times area of triangle ABC+3\times 2+1\left (2+3\right )
Simplify
12=2\times area of triangle ABC+6+5
12=2\times area of triangle ABC+11
1=2\times area of triangle ABC
area of triangle ABC=\frac{1}{2}
Answer: \frac{1}{2} square unit.

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About mvtrinh

Retired high school math teacher.
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