Determine whether a semiregular uniform tessellation can be created from the given shapes, with all sides 1 unit long. If so determine the number of each shape needed at each vertex to create the tessellation.

regular pentagons and squares


Answered 1 year ago
Answered 1 year ago
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Let xx represent the measure of an interior angle of a regular pentagon where nn is the number of sides of the polygon.

x=180(n2)n=180(52)5=180(3)5=5405=108\begin{aligned} x &= \frac{180(n-2)}{n}\\ &= \frac{180(5-2)}{5}\\ &= \frac{180(3)}{5}\\ &= \frac{540}{5}\\ &= 108\\ \end{aligned}

The interior angle is 108108^{\circ}.

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