## Determine the rectangle's area (Semi-circle and rectangle)

Home -> Solved problems -> Calculate the rectangle’s area ### Solution

At first, we add some sections to the semi-circle and the rectangle like it is shown in the next figure Using Pythagoras theorem in the triangle $$\triangle MAB$$, we get $\begin{array}{r} (r+x)^{2}+y^{2}=6^{2} \\ =36 \\ r^{2}+2 r x+x^{2}+y^{2}=36 \end{array}$ $$x^{2}+y^{2}=r^{2}$$ : Circle equation at the point $$M$$, thus $\begin{array}{r} r^{2}+2 r x+r^{2}=36 \\ 2r^{2}+2rx=36 \\ r^{2}+rx=18 \\ r(r+x)=18 \\ \Rightarrow BC\cdot AB=18 \end{array}$
Home -> Solved problems -> Calculate the rectangle’s area

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Home -> Solved problems -> Calculate the rectangle’s area