ANSWER
The perimeter of the polygon is 91 units.
EXPLANATION
A regular heptagon has seven equal sides.
The perimeter can be calculated by multiplying one side by 7.
Since we know two consecutive vertices, we can find the length of one side using the distance formula
[tex]|AB|= \sqrt{ {(4 - - 1)}^{2} + {(10 - - 2)}^{2} } [/tex]
[tex]|AB|= \sqrt{ {(4 + 1)}^{2} + {(10 + 2)}^{2} } [/tex]
[tex]|AB|= \sqrt{ {(5)}^{2} + {(12)}^{2} } [/tex]
[tex]|AB|= \sqrt{ 25+ 144 } [/tex]
[tex]|AB|= \sqrt{ 169 } = 13units[/tex]
The perimeter is therefore
[tex] = 7 \times 13 = 91units[/tex]
