Question

Follow the steps to find the area of the shaded region

Answer 1

Step 1:

From the figure

`\begin{gathered} x\text{ + 129 = 180 \lparen sum of angles on a straight line\rparen} \\ \\ x\text{ = 180 - 129} \\ \\ x\text{ = 51} \end{gathered}`

Step 2

`\begin{gathered} sin\text{ x = }(Opposite)/(Hypotenuse) \\ sin51\text{ = }(h)/(8) \\ \\ 0.777\text{ = }(h)/(8) \\ h\text{ = 8 }*\text{ 0.777} \\ \\ h\text{ = 6.22cm} \end{gathered}`

Step 3

`\begin{gathered} Area\text{ of a triangle = }(1)/(2)\text{ }*\text{ base }*\text{ h} \\ \\ =\text{ }(1)/(2)\text{ }*\text{ 6.22 }*8 \\ \\ Area\text{ of a triangle = 24.9 cm}^2 \end{gathered}`

Step 4

`\begin{gathered} Area\text{ of a sector = }(\theta)/(360)\text{ }*\pi r^2 \\ \\ =\text{ }(129)/(360)\text{ }*\text{ }(22)/(7)\text{ }*\text{ 8}^2 \\ \\ =\text{ 72.08 cm}^2 \end{gathered}`

Area of the shaded part = 72.08 - 24.9 = 47.18

Final answer

`\begin{gathered} Angle\text{ x = \lbrack51\rbrack} \\ \\ Area\text{ of the shaded part = 47.2 cm}^2 \end{gathered}`