we know that the area of a regular hexagon=(Perimeter*Apothem)/2
step 1 find the perimeter P=6*b where b is the side length b=10 m so P=6*10-----> P=60 m
step 2
Find the apothem Applying the Pythagorean Theorem
c²=a²+b²------> a²=c²-b² where a is the apothem b=10/2-----> 5 m c=10 m so a²=10²-5²------> a²=100-25-----> a=√75 m apothem=√75 m
step 3 find the area of a regular hexagon the area of a regular hexagon=(Perimeter*Apothem)/2 the area of a regular hexagon=[60*√75]/2------> 30√75 -------> 150√3 m²
the answer is the area of a regular hexagon is 150√3 m²
