# In triangle ABC DE – middle line. The area of triangle ADE is 7. Find the area of triangle ABC.

The middle line of a triangle cuts off a similar triangle from it, its area is equal to 1/4 of the area of ​​the original triangle.
Since DE is the middle line △ ABC, the area △ ADE that it cuts off is equal to 1/4 of the area площади ABC:
S △ ADE = S △ ABC / 4.
Substitute the area площади ADE given by condition and find the area △ ABC:
S △ ABC / 4 = 7;
S △ ABC = 4 * 7 (by proportion: to find the unknown numerator of the first fraction (S △ ABC), you need to multiply the denominator of the first fraction (4) by the numerator of the second fraction and divide by the denominator of the second fraction (the number 7 is a fraction with numerator 7 and denominator 1));
S △ ABC = 28.
Answer: S △ ABC = 28.

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