Question

All of the triangles in the figure below are congruent. What is the area of the figure? Note that all measurements are in centimeters.
Note that the apothem shown is equal to 2 square root of three.

24square root of three.cm2

36 + 24square root of three.cm2

36 square root of three.cm2

24 + 36square root of three.cm2

Answer 1

Area of a triangle is (1/2)(base)(height)
Each small triangle has area equal to (1/2)(4)(3)=6 sq. cm.
There are 6 triangles, so 6*6=36 sq. cm.
The area of a regular hexagon is (1/2)(apothem)(perimeter)
In your example, this is (1/2)(2root3)(4*6)= 24root3 sq. cm.

Answer 2

Wow, thank you so much! Perfect explanation!