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nikklg [1K]
1 year ago
12

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

haded.
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
Mathematics
2 answers:
Kay [80]1 year ago
8 0

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.

<h3>Find the expression for the area of the shaded regions:</h3>

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

#SPJ1

tatiyna1 year ago
8 0

Answer:

Regular Hexagon

Regular Pentagon

Square

Equilateral Triangle

Step-by-step explanation:

E2020 Geometry B!! :3

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