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

1. Regular Hexagon
Regular Pentagon
Square
Equilateral Triangle
Step-by-step explanation:
E2020 Geometry B!! :3

2. thongdat2
Shaded area = area of the hexagon – area of the pentagon + area of the square – area of the equilateral triangle. This can be obtained by finding each shaded area and then adding them.

### Find the expression for the area of the shaded regions:

From the question we can say that the Hexagon has three shapes inside it,
• Pentagon
• Square
• Triangle
Also it is given that,
An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon.
From this we know that equilateral triangle is the smallest, then square, then regular pentagon and then a regular hexagon.
A pentagon is shown inside a regular hexagon.
• Area of first shaded region = Area of the hexagon – Area of pentagon
An equilateral triangle is shown inside a square.
• Area of second shaded region = Area of the square – Area of equilateral triangle
The expression for total shaded region would be written as,