Question

Find the area of the shaded region.8005 cmA = [?] cm2Enter a decimal rounded to the nearest tenth.

Answer 1

The unshaded area can be calculated by subtracting the area of the triangle from the area of the minor sector.

The area of the sector with angle 80 degrees is given by,

`\begin{gathered} A_s=(\theta)/(360)*\pi r^2 \\ A_s=(80)/(360)*\pi(5)^2 \\ A_s\approx17.4534 \end{gathered}`

The triangle is an isosceles triangle with base and height as follows,

`\begin{gathered} \text{Base}=2*(5\sin 40^(\circ))\approx6.4279 \\ \text{ Height=}5\cos 40^(\circ)\approx3.8302 \end{gathered}`

So the area of the triangle is given by,