Answer:
[tex] A=(8 \pi +40) cm^2 [/tex]
[tex] P=(4 \pi + 4\sqrt {29}) \: cm[/tex]
Step-by-step explanation:
For semicircle:
Diameter = 8 cm
Radius (r) = 8/2 = 4 cm
For triangle:
Base (b) = 8 cm
Height (h) = 10 cm
Area of the shaded region
[tex] A=\frac {1}{2} \pi r^2 +\frac {1}{2}b.h[/tex]
[tex] A=\frac {1}{2} \pi (4)^2 +\frac {1}{2}(8).(10)[/tex]
[tex] A=(8 \pi +40) cm^2 [/tex]
By Pythagoras Theorem:
[tex] AC = BC = \sqrt {4^2 +10^2}[/tex]
[tex] AC = BC = \sqrt {16 +100}[/tex]
[tex] AC = BC = \sqrt {116}[/tex]
[tex] AC = BC =2\sqrt {29}[/tex]
[tex] P= \frac {1}{2} \times 2\pi r+ AC + BC[/tex]
[tex] P= \pi (4)+ 2\sqrt {29} + 2\sqrt {29}[/tex]
[tex] P=(4 \pi + 4\sqrt {29}) \: cm[/tex]
