求边长为 7 cm 的正六边形的面积。答 ... cm^2 求正十五边形的内角。答 ...

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完整解法

1. Recognise the regular hexagon as 6 equilateral triangles and set up the area calculation

A regular hexagon can be divided into 6 congruent equilateral triangles, each with side $7\text{ cm}$ .

Area of one equilateral triangle:
$\frac{\sqrt{3}}{4}s^2=\frac{\sqrt{3}}{4}(7)^2$

Area of hexagon:
$6\times \frac{\sqrt{3}}{4}(7)^2$

2. Evaluate the area and round suitably

$6\times \frac{\sqrt{3}}{4}\times 49=127.3057\ldots$

So the area is approximately
$127\text{ cm}^2$

答案

$127\text{ cm}^2$

1. Substitute $n=15$ into the formula for the interior angle of a regular polygon and evaluate

For a regular $15$ -sided polygon,
$\text{interior angle}=\frac{(15-2)\times 180^\circ}{15}=\frac{13\times 180^\circ}{15}=156^\circ.$

答案

$156^\circ$

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