the hexagon is composed of six equilateral triangles
the apothem is the altitude of one of the triangles
the area is the sum of the triangles' areas
find the apothem, in meters, and area, in square meters, of a regular hexagon with side length 7 m. round to the nearest hundredth
2 answers
Concentrate on just one of the six congruent isosceles triangles
For each one:
the central angle is 60° and the two base angles are equal,
ahhh, so each triangle is equilateral.
each side in such a triangle is 7 m
The apothem is the perpendicular to one of the sides, let's call it a
a/7 = sin60
a = 7(√3/2) = ....
area of 1 triangle = (1/2)(base)(height)
= (1/2)(7)(7√3/2) = ....
so the whole hexagon is 6 times that area
For each one:
the central angle is 60° and the two base angles are equal,
ahhh, so each triangle is equilateral.
each side in such a triangle is 7 m
The apothem is the perpendicular to one of the sides, let's call it a
a/7 = sin60
a = 7(√3/2) = ....
area of 1 triangle = (1/2)(base)(height)
= (1/2)(7)(7√3/2) = ....
so the whole hexagon is 6 times that area
1 answer