ABC is a right-angled triangle with right angle at B. If the semi-circ

1.	ABC is a right-angled triangle with right angle at B. If the semi-circle on AB with AB as diameter encloses an area of 81 sq.cm and semi-circle on BC with BC as diameter encloses an area of 36 sq.cm then the area of the semi-circle on AC with AC as diameter will be
Answer» $\huge\mathcal\red{SolutiOn:}$ $\sf{Given-}$ ABC is a right-angled triangle with right ANGLE at B. If the semi-circle on AB with AB as DIAMETER encloses an AREA of 81 sq.cm. Semi-circle on BC with BC as diameter encloses an area of 36 sq.cm then the area of the semi-circle on AC with AC. $\sf\red{We~have~to~find~the~diameter~and~semicircle~on~AC:}$ $\sf{Required~area=}\:\frac{1}{2}\:\pi \sf{r^2=\frac{1}{2}}\pi × (\frac{AC}{2})^2\\~~~~~~~~~~~~~=\frac{\pi}{8}\:\:AC^2\\~~~~~~~~~~~~~~~~~~~~~~~~~~~=\frac{\pi}{8}\:(AB^2+BC^2)\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\frac{1}{2}\:\pi\:(\frac{AB}{2})^2+\frac{1}{2}\:\pi(\frac{BC}{2})^2\\~~~~~~~~~~~~~~~~~~=\mathtt{81+36}\\~~~~~~~~~~~~~~~~~~=\mathtt{117cm^2}$ $\sf{You~can ~see~ the~ first~part} \:\frac{1}{2}\pi(\frac{AB}{2})^2\:\sf{this~is~the~area~}\\\sf{and~AB~as~the~diameter}\\\bold{Similarly,}$ $\sf{The~second~part}~\frac{1}{2}\pi(\frac{BC}{2})^2\sf{~is~the~area~of~the~semi-circle~}\\\sf{and,~BC~as~the~diameter}$ $\sf\purple{∴~the~area~of~the~semi-circle,}$ $\sf\purple{~on~AC~with~AC~as ~diameter~will~be~177cm^2.}$ _______________________________________ $\huge\underline\mathfrak\pink{Brainliest~plzz!}$

ABC is a right-angled triangle with right angle at B. If the semi-circle on AB with AB as diameter encloses an area of 81 sq.cm and semi-circle on BC with BC as diameter encloses an area of 36 sq.cm then the area of the semi-circle on AC with AC as diameter will be

Answer»

$\huge\mathcal\red{SolutiOn:}$

$\sf{Given-}$

ABC is a right-angled triangle with right ANGLE at B.
If the semi-circle on AB with AB as DIAMETER encloses an AREA of 81 sq.cm.
Semi-circle on BC with BC as diameter encloses an area of 36 sq.cm then the area of the semi-circle on AC with AC.

$\sf\red{We~have~to~find~the~diameter~and~semicircle~on~AC:}$

$\sf{Required~area=}\:\frac{1}{2}\:\pi \sf{r^2=\frac{1}{2}}\pi × (\frac{AC}{2})^2\\~~~~~~~~~~~~~=\frac{\pi}{8}\:\:AC^2\\~~~~~~~~~~~~~~~~~~~~~~~~~~~=\frac{\pi}{8}\:(AB^2+BC^2)\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\frac{1}{2}\:\pi\:(\frac{AB}{2})^2+\frac{1}{2}\:\pi(\frac{BC}{2})^2\\~~~~~~~~~~~~~~~~~~=\mathtt{81+36}\\~~~~~~~~~~~~~~~~~~=\mathtt{117cm^2}$