Question 1121096: In a triangle ABC, D is a point on side AB and E is the point on AC.
DE parallel to BC. DE= 1/3 BC.
Construct a line from D to C.
Area of triangle ADE is 20cm²
Find the area of triangle DEC?
Answer by greenestamps(13206)   (Show Source):
You can put this solution on YOUR website!
Triangles ADE and ABC are similar; DE = (1/3)*BC, so the ratio of similarity is 1:3.
The ratio of areas is then the square of that, 1:9.
Given that the area of triangle ADE is 20, the area of triangle ABC is then 20*9 = 180.
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.
So the area of triangle ADC is (1/3)*180 = 60.
Finally, the area of triangle DEC is 60-20 = 40.
Answer: The area of triangle DEC is 40 cm^2.
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