A regular hexagon (ABCDEF) shape of city center in Egypt with sides all of lenght 4 km and with center at 0 (letter). The interior angles of the hexagon are all equal. The interior angles of a polygon with n equal sides and n equal angles (regular polygon) add up to (n-2) x 180 degrees.

Question

A regular hexagon (ABCDEF) shape of city center in Egypt with sides all of lenght 4 km and with center at 0 (letter). The interior angles of the hexagon are all equal. The interior angles of a polygon with n equal sides and n equal angles (regular polygon) add up to (n-2) x 180 degrees.
a.) Calculate the size of angle ABC.
b.) Given that OB=OC=BC, find the area of the triangle OBC
c.) Find the area of the whole city center.

oobleck · Answer

(a) since there are 6 of them, 4*180/6 = 120
(b) Draw the diagram, and you will see lots o f 30,60,90-degree angles
(c) there are 6 equilateral triangles of side 4. You know how to find the area of an equilateral triangle, right?