Question 1121096
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Triangles ADE and ABC are similar; DE = (1/3)*BC, so the ratio of similarity is 1:3.<br>
The ratio of areas is then the square of that, 1:9.<br>
Given that the area of triangle ADE is 20, the area of triangle ABC is then 20*9 = 180.<br>
AD and AB are corresponding sides of the similar triangles, so AD = (1/3)*AB.  That means the area of triangle ADC is (1/3) the area of triangle ABC, because the heights of the two triangles (the perpendicular distance from line AB to point C) are the same.<br>
So the area of triangle ADC is (1/3)*180 = 60.<br>
Finally, the area of triangle DEC is 60-20 = 40.<br>
Answer: The area of triangle DEC is 40 cm^2.