Question

Please help and explain how you got it

Answer 1

check the picture below.

notice, the figure is just, a triangle with a base of 3 and an altitude of 4, a rectangle of 4x7, and a semi-circle with a diameter of 4.


`\bf \textit{area of a circle}\\\\ A=\pi r^2\qquad \begin{cases} d=diameter\\ r=radius=(d)/(2)\\ -------\\ d=4\\ r=2 \end{cases}\implies \begin{array}{llll} A=\pi 2^2\implies A=4\pi\\\\ \textit{area of half that circle}\\\\ A_h=\cfrac{4\pi }{2}\implies A_h=2\pi \end{array} \\\\ -----------------------------\\\\ \stackrel{\textit{area of triangle}}{(1)/(2)\cdot 3\cdot 4}+\stackrel{\textit{area of the rectangle}}{4\cdot 7}+\stackrel{\textit{area of the semi-circle}}{2\pi } \\\\\\ 6~~+~~28~~+~~2\pi`