AREA OF SHAPES
CONTENT
- Area of a Circle
- Area of a Triangle
- Area of a Square
- Area of a Rectangle
- Area of a Parallelogram
- Area of a Trapezium
- Area of Irregular Shapes
Area of a Circle
Area of a circle \(= πr^2\)
Where \(π = \frac{22}{7}\)
Diameter \(= 2r\), where \(r = radius\)
Example:
1. Find the area of a circle whose radius is \(3\frac{1}{2}m\). (Take \(π\) to be \(\frac{22}{7}\))
Solution:
Area of a circle \(= πr^2\)
\(\frac{22}{7} × (3 \frac{1}{2})^2 \\= \frac{22}{7} × \frac{7}{2} × \frac{7}{2} \\ = \frac{11×7}{2} \\ = \frac{77}{2}m^2 = 38.5m^2\)
2. The area of a circle is \(126.5cm^2\). Find its radius correct to \(2\) decimal places.
Solution:
Area of circle \(= πr^2\)
\(126.5cm^2 = \frac{22}{7} r^2 \\ \frac{253}{2} = \frac{22}{7} r^2 \\ 253 × 7 = 22 × 2 × r^2 \\ r^2 = \frac{161}{4} \\ r = \sqrt{\frac{161}{4}} \\ r = \frac{12.689}{2} \\ r = 6.345 \\ r = 6.35 (2 d.p.) \)
Area of a Triangle
Any diagonal of a rectangle divided into two equal right-angled triangles forms a right-angled triangle.
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