Answer:
3.75 in
Step-by-step explanation:
Since this figure is regular (all of the sides are congruent), the length of each side would be the perimeter, 7.5, divided by the number of sides, 6:
7.5/6 = 1.25 in.
To find the length across one entire hexagon:
We can draw 6 small triangles from the center of the hexagon. We will work with the triangle at the bottom.
The top vertex of this triangle will be 60°; this is because there are 6 angles, and 360 (the amount of a complete rotation around the center point) divided by 6 is 60°.
This will be an isosceles triangle. The top vertex of this triangle is in the center of the hexagon; this means the length of the segment connecting this vertex to the bottom two vertices of the triangle will be the same. (Think of it as the radius of a circle, the same from the center to every outside point.)
The sum of the measures of the angles in a triangle is 180°; taking out the top angle, we have 180-60 = 120°. Since the triangle is isosceles, the base angles will be equal:
120/2 = 60
The bottom two angles will also be 60°. This makes the triangle equiangular, which also makes it equilateral; all 3 sides will be 1.25.
This means across the dotted line we have 1.25+1.25+1.25 = 3.75.
