The hexagon below is made up of six equilateral triangles with sides of 6 centimeters each. The height of each triangle is 5.2 centimeters. What is the area of the hexagon
area of each triangle = (1/2)(6)(5.2) = 15.6
There are 6 of those, so
total area = 6(15.6) 93.6 cm^2
To find the area of the hexagon, we need to first find the area of one equilateral triangle, and then multiply it by six since there are six equilateral triangles in the hexagon.
The formula to find the area of an equilateral triangle is A = (sqrt(3) / 4) * s^2, where A is the area and s is the length of the side.
In this case, the length of the side is 6 centimeters, so we can substitute it into the formula.
A = (sqrt(3) / 4) * 6^2
= (sqrt(3) / 4) * 36
≈ (1.732 / 4) * 36
≈ 0.433 * 36
≈ 15.588
So the area of one equilateral triangle is approximately 15.588 square centimeters.
Since there are six equilateral triangles in the hexagon, we can now multiply the area of one triangle by 6.
Area of the hexagon = 15.588 * 6
≈ 93.528
Therefore, the area of the hexagon is approximately 93.528 square centimeters.