[tex]\Large\mathtt{\fcolorbox{lime}{black}{\pink{ANSWER}}}[/tex]
In the following figure, ABCD is a square and is a diameter of the circle centered at 0. If the area of the square is 100, what is the area of the shaded region?
︎︎ ︎︎ ︎︎ ︎︎• 25π/2
︎︎ ︎︎ ︎︎ ︎︎ ︎︎ ︎︎• ︎︎25π
︎︎ ︎︎ ︎︎ ︎︎ ︎︎ ︎︎• ︎︎ ︎︎50π
︎︎ ︎︎ ︎︎ ︎︎ ︎︎ ︎︎• ︎︎5π/2
[tex]\begin{gathered}\\ \begin{gathered}\rm { \large\pink{Explanation:}} \\ \green{\boxed{ \boxed{ \begin{array}{c}\tt{} \pink{⊱ ────────────── ✯ ────────────── ⊰} \\\sf{}The \: area \: of \: the \: square \: is \: 100, \: so \: each \: side \\ \sf{}of \: the \: square \: is \: 10 \: (because \: 102= 100). The \\ \sf{}diameter \: of \: the \: circle \: is \: 10, \: so \: its \: radius \: is \: 5. \\ \sf{} \pink{\underline{Plug \: this \: value \: into \: the \: area \: formula \: for}} \\ \sf{} \pink{\underline{a \: circle: \: A = \pi r2 = \pi(5)2 = 25\pi . }} \: The \: shaded \\ \sf{}region \: is \: half \: of \: this \: area, \: which \: is \: 25\pi /2
.\\ \pink{⊱ ────────────── ✯ ────────────── ⊰ }\\\end{array}}}}\end{gathered}\end{gathered}[/tex]
