1 Answer

Karthick Aravindan · Answer 1 · 2022-06-01T21:07:58+0000

Answer:

$A=(8 \pi +40) cm^2$

$P=(4 \pi + 4\sqrt {29}) \: cm$

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

$A=\frac {1}{2} \pi r^2 +\frac {1}{2}b.h$

$A=\frac {1}{2} \pi (4)^2 +\frac {1}{2}(8).(10)$

$A=(8 \pi +40) cm^2$

By Pythagoras Theorem:

$AC = BC = \sqrt {4^2 +10^2}$

$AC = BC = \sqrt {16 +100}$

$AC = BC = \sqrt {116}$

$AC = BC =2\sqrt {29}$

$P= \frac {1}{2} * 2\pi r+ AC + BC$

$P= \pi (4)+ 2\sqrt {29} + 2\sqrt {29}$

$P=(4 \pi + 4\sqrt {29}) \: cm$

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