Answer:
59.44 units²
Step-by-step explanation:
The area of each triangular section can be computed from the side length (5 units) and the central angle (72°) as ...
... section area = (1/2)sin(72°)·5² ≈ 12.5·0.951057 ≈ 11.8882 . . . units²
Then 5 such sections will have an area of ...
... pentagon area = 5·11.8882 units² = 59.4410 units²
_____
<em>Comment on central angle</em>
The central angles total 360°. There are 5 equal sections, so the central angle for each of them is 360°/5 = 72°.
<em>Comment on area formula</em>
It can be occasionally handy to know that the area of a triangle can be computed from the lengths of adjacent sides and the angle between them. The formula for sides of length "a" and "b" and angle β is ...
... A = (1/2)ab·sin(β)
