Question

An equilateral is shown inside a square inside a regular pentagon inside a regular hexagon. The square and regular hexagon are shaded.
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.

Shaded area = area of the
– area of the
+ area of the
– area of the

Answer 1

Shaded area = area of the regular hexagon − area of the regular pentagon + area of the square − area of the equilateral triangle.

Reason: start with the outer shaded hexagon, remove the unshaded pentagon inside it, add the shaded square inside the pentagon, then remove the unshaded triangle inside the square.