Respectively 64404

In the triangle, ABC, X, and Y are the centers of the sides BC and CA, respectively. The ABXY trapezoid has an area of 12. Calculate the area of triangle ABC.

Correct answer:

S₂ =  16

Step-by-step explanation:

$$\begin{gathered} S_1=12 \\ {S}_2=\frac{av}{2} \\ {S}_1=\frac{a+(a/2)}{2}\cdot v/2 \\ {S}_1=\frac{1+(1/2)}{2}\cdot av/2 \\ {S}_1=\frac{1+1/2}{2}\cdot S_2 \\ {S}_2=\frac{S_1}{\frac{1+1/2}{2}}=\frac{12}{\frac{1+1/2}{2}}=16 \end{gathered}$$

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