Question

Find the perimeter and area of the shaded region in the adjoining figure, it being given that OAB is an
equilateral triangle of side 28 cm and one end is a semi-circle on AB as a diameter.

Answer 1

(196√3+308) cm square will be the

Answer 2

Answer:

Step-by-step explanation:

The triangle is an equilateral triangle with side=28 cm and the diameter of the semi circle is the side of an equilateral triangle, therefore, AB=28 cm

Now, Perimeter of the shaded region= Perimeter of Equilateral triangle+ Perimeter of Semicircle

=$\frac{{\pi}d}{2}+3(side)$

=$\frac{22}{7}{\times}\frac{28}{2}+3(28)$

=$44+84$

=$128 cm$

Also, Area of the shaded region=Area of the triangle+ Area of the semicircle

=$\frac{\sqrt{3}}{4}a^{2}+\frac{{\pi}r^{2}}{2}$

=$\frac{\sqrt{3}}{4}{\times}28{\times}28+\frac{{\pi}{\times}14{\times}14}{2}$

=$196\sqrt{3}+\frac{22}{7}{\times}7{\times}14$

=$(196\sqrt{3}+308)cm^{2}$