Question

35. In the Fig if AB=16cm and BC=12cm
Calculate the area of the shaded region in the figure :
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Answer 1

Answer:

$96-16\pi cm^2$.

Step-by-step explanation:

We have been given the AB= $16cm$ and BC= $12cm$.To find the area of the shaded region,at first we use pythagorous thorem and after that we find area of triangle are shown below:

$AC^2 = AB^2 + BC^2\\AC^2 = 16^2 + 12^2$

$AC^2 = 400\\AC = 20 cm$

Find area of triangle

$= \frac{1}{2}*16*12 = 96 cm^2$

find the area of triangle for every side=

$\frac{1}{2} *16*r +\frac{1}{2}*12*r + \frac{1}{2}*20*r$

$=24r$

Equate the result of both the triangle

$\\24r=96\\r=4$

Find the area of circle

$\pi r^2 = 16\pi$

Thus,the area of the shaded region=$96 - 16\pi cm^2$