Hexagon Area Calculation
The problem asks for the approximate area of a regular hexagon inscribed within a circle. The radius of the circle is given as 21 cm.
Relating Hexagon to Circle
A regular hexagon inscribed in a circle can be divided into 6 equilateral triangles. The side length of each equilateral triangle is equal to the radius of the circle.
- Radius of the circle, $r = 21$ cm.
- Side length of the hexagon, $s = r = 21$ cm.
Area Formula for Hexagon
The area of a regular hexagon can be calculated using the formula:
Area = $\frac{3\sqrt{3}}{2} s^2$, where $s$ is the side length.
Calculating the Hexagon's Area
Substitute the side length ($s = 21$ cm) into the formula:
- Area = $\frac{3\sqrt{3}}{2} \times (21 \text{ cm})^2$
- Area = $\frac{3\sqrt{3}}{2} \times 441 \text{ cm}^2$
- Area = $\frac{1323\sqrt{3}}{2} \text{ cm}^2$
Now, using the approximate value of $\sqrt{3} \approx 1.732$:
- Area $\approx \frac{1323 \times 1.732}{2} \text{ cm}^2$
- Area $\approx \frac{2291.556}{2} \text{ cm}^2$
- Area $\approx 1145.778 \text{ cm}^2$
Final Approximation and Answer Choice
The calculated approximate area is $1145.778 \text{ cm}^2$. Comparing this to the given options, the closest value is 1145 $cm^2$.
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Calculate the area of the triangle whose sides are 8 cm, 9 cm and 13 cm. (Rounded up to two decimal places)
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