Question

the shape is formed from two straight lines and two arcs. work out the total shaded area correct to the nearest 0.1cm^2.

Answer 1

Check the picture below.

so we're really looking for the area of a sector of a circle with 63° and a radius of 3, twice.

`\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =63\\ r=3 \end{cases}\implies A=\cfrac{(63)\pi (3)^2}{360} \\\\\\ A=\cfrac{63\pi }{40}\implies \stackrel{\textit{now let's double that}}{2\cdot \cfrac{63\pi }{40}}\implies \cfrac{63\pi }{20}\implies 9.9~cm^2`