Additional Mathematics – Circular measure | e-Consult

Answer 3

Step 1 – Area of the whole circle:

\[

A_{\text{circle}} = \pi r^{2} = \pi \times 6^{2} = 36\pi\ \text{m}^{2}

\]

Step 2 – Area of the removed sector:

\[

A_{\text{sector}} = \frac{1}{2}r^{2}\theta

= \frac{1}{2}\times 6^{2}\times\frac{\pi}{2}

= \frac{1}{2}\times 36\times\frac{\pi}{2}

= 9\pi\ \text{m}^{2}

\]

Step 3 – Remaining circular area:

\[

A_{\text{remaining}} = 36\pi - 9\pi = 27\pi\ \text{m}^{2}

\]

Step 4 – Area of the rectangular patio:

\[

A_{\text{rect}} = \text{width}\times\text{length}=6\times10=60\ \text{m}^{2}

\]

Step 5 – Total area:

Thus the combined area is \(\displaystyle 27\pi + 60\) m², which is approximately 144.82 m².