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

Answers

  2. 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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