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

January 15, 2021 | education

| 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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