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

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]

Answer 2

The expression would be written as

Area of hexagon - Area of the pentagon + Area of the square - area of the rectangle.

We can see that the Hexagon has three shapes inside it

• Pentagon
• Square
• Rectangle

We have to find the areas of each of these shapes and perform basic arithmetic to find the area of the shaded regions.

Read more on the area of a shape here:

https://brainly.com/question/16501078