Matematik SPM 2018, Kertas 2 (Soalan 11)

Soalan 11 (6 markah):
Rajah 8 menunjukkan sektor OABC dan sektor ODE masing-masing dengan pusat sepunya O.

Hitung
(a) perimeter, dalam cm, seluruh rajah itu,
(b) luas, dalam cm², kawasan berlorek.
Penyelesaian:
(a)
$\begin{array}{l}\text{Perimeter seluruh Rajah}\\ =OP+PE+\text{Arc }DE+DC\\ +\text{Arc }CBA+AO\\ =10+5+\left(\frac{{50}^o}{{360}^o}\times 2\times \frac{22}{7}\times 15\right)+5\\ +\left(\frac{{230}^o}{{360}^o}\times 2\times \frac{22}{7}\times 10\right)+10\\ =30+\frac{275}{21}+\frac{2530}{63}\\ =\frac{5245}{63}\\ =83.254\text{ cm}\end{array}$
(b)
$\begin{array}{l}\text{Luas kawasan berlorek}\\ =\left(\frac{{230}^o}{{360}^o}\times \frac{22}{7}\times {10}^2\right)\\ +\left[\left(\frac{{50}^o}{{360}^o}\times \frac{22}{7}\times {15}^2\right)-\left(\frac{{50}^o}{{360}^o}\times \frac{22}{7}\times {10}^2\right)\right]\\ =\frac{12650}{63}+\left(\frac{1375}{14}-\frac{2750}{63}\right)\\ =\frac{3575}{14}\\ =255.36{\text{ cm}}^2\end{array}$