Question

The star shape is made from a regular hexagon and six congruent equilateral triangles The area of the star shape is 96cm squared Work out the area of the regular hexagon.

Answer 1

Answer:

48 Square Centimeters

Step-by-step explanation:

The red triangular exterior pieces are all equilateral triangles with some side length.

We don't need to know what that side length is. It doesn't matter.

The area of one red equilateral triangle is some area A.

There are 6 of these red triangles, so the red exterior triangular parts combine to a total area of 6*A.

The hexagon is composed of equilateral triangles as well.

Each of these blue equilateral triangles is congruent to any outer red triangle because the side length is the same.

Therefore, the 6 blue equilateral triangles composing this hexagon combine to get a total area of 6*A

The area of the star overall is 12*A because we have 6 blue triangles combining with the 6 red triangles.

There is a total of 12 triangles.