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 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,

Shaded area = Area of first shaded region + Area of second shaded region

Hence,        

⇒ Shaded area  = area of the hexagon – area of the pentagon + area of the  square – area of the equilateral triangle.

 

Learn more about area of a shape here:

brainly.com/question/16501078

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