Question

an equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon. write an expression for the area of the shaded regions.

Answer 1

The Correct answers are:

C: Regular Hexagon

B: Regular Pentagon

B: Square

A: Equilateral Triangle

(The question above doesn't make it instantly clear which answer is correct at all. Hopefully, this answer makes it a bit easier to understand what are the correct answers to this question.

Answer 2

we know that
the area of the shaded regions is equal to
area of the shaded region 1+area of the shaded region 2

step 1
find the area of the shaded region 1
area of the shaded region 1=Area regular Hexagon-Area regular Pentagon

step 2
find the area of the shaded region 2
area of the shaded region 2=Area of a square-Area of the equilateral triangle

therefore
the area of the shaded regions is equal to
[Area regular Hexagon-Area regular Pentagon]+[Area of a square-Area of the equilateral triangle]