Recall, the area of a circle is given as \( \scriptsize \pi r^2 \)

In general, the area of a sector of a circle is proportional to the angle of the sector as shown in the diagram above i.e. the area of the sector XOY is \( \frac{\theta}{360^o} \) of the whole circle

i.e. Area of Sector XOY = \( \frac {θ}{360} \scriptsize \: \times \: \pi r^2 \)

### Example 1.3.1:

A pie chart is divided into four sectors as shown in the diagram below. Each sector represents a percentage of the whole. The two larger sectors are equal and each represents X%. What is the angle subtended by one of those larger sectors? **(WAEC)**

**Solution:**

**Note:** x% + x% + 21 + 9 = 100%

i.e. 2x% = 100 – 30

i.e. x% = \( \frac{70}{2}\) = 35%

x% = 35%

by proportions 35% ≡ x°

100% = 360º

x° = \( \scriptsize 36^o \: \times \: \normalsize \frac{35}{100} \\ \scriptsize 18^o \: \times \: 7^o \\ \scriptsize 126^o \)

### Example 1.3.2:

In the diagram below, ABCD is a rhombus with dimensions as shown BXD is a circular arc with centre A. Calculate the area of the shaded section to the nearest cm^{2.}

**Solution**

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