Flowerbed

The family has tulips on a square flower bed of 6 meters. Later, they added a square terrace with a side of 7 meters to their house. One vertex of the terrace lay exactly in the middle of a tulip bed, and one side of the terrace was divided by the side of the tulip bed in a ratio of 1:5.
In what proportion did the other side of the terrace split the other side of the flower bed? How many square meters of terraces have their tulips shrunk?

Correct answer:

M = 1:5
S =  9 m²

Step-by-step explanation:

$M=1:5$

$$\begin{gathered} a=6 \\ b=a/2=6/2=3 \\ A=b\cdot (b-1)/2=3\cdot (3-1)/2=3{\text{m}}^2 \\ B=b\cdot b=3\cdot 3=9{\text{m}}^2 \\ S=B-A+A=9-3+3=9{\text{m}}^2 \end{gathered}$$

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