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