Question

Find the area of the shaded region. Round your answer to the nearest tenth. radius = 6cm

Answer 1

Given

radius of the circle = 6cm

Angle subtended by the inscribed triangle = 120 degres

The formulae below would help ss solve the problem:

`\begin{gathered} Area\text{ of sector = }(\theta)/(360)\text{ }*\pi r^2 \\ Where\text{ r is the radius} \\ \\ Area\text{ of a triangle = }(1)/(2)absin\theta \end{gathered}`

The area of th sahaded part can be found using the formula:

`Area\text{ of shaded part = Area of half circle - Area of the triangle}`

Substituting the given values:

`\begin{gathered} Area\text{ of shaded part = }(120)/(360)\text{ }*\text{ }\pi*6^2\text{ - }(1)/(2)\text{ }*\text{ 6}*6* sin120 \\ =\text{ 37.6991 - 15.5885} \\ =\text{ 22.1106} \\ \approx\text{ 22.1 cm}^2 \end{gathered}`

Answer: 22.1 square cm