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21 July, 18:13

The length of one side of a regular hexagon is x. A regular pentagon also has a side length of x. A square is constructed with a side length of x. What is the total perimeter of all three figures.

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  1. 21 July, 18:29
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    The total perimeter of all three figure is 15 x.

    Step-by-step explanation:

    Given as:

    The side length of regular hexagon = x

    The side length of regular pentagon = x

    The side length of square = x

    A regular hexagon is that polygon whose number of sides is 6

    A regular pentagon is that polygon whose number of sides is 5

    A square is that polygon whose number of sides is 4

    Now,

    Perimeter - A perimeter is define as the total distance around any polygon

    So, perimeter of hexagon with sides 6 = sum of all the six sides

    Or, perimeter of hexagon with sides 6 = x+x+x+x+x+x = 6 x

    perimeter of pentagon with sides 5 = sum of all the five sides

    Or, perimeter of pentagon with sides 5 = x+x+x+x+x = 5 x

    And, perimeter of square with sides 4 = sum of all the four sides

    Or, perimeter of square with sides 4 = x+x+x+x = 4 x

    So, The total perimeter of all three figures = perimeter of hexagon + perimeter of pentagon + perimeter of square

    ∴ The total perimeter of all three figures = 6 x + 5 x + 4 x

    I. e The total perimeter of all three figures = 15 x

    Hence The total perimeter of all three figure is 15 x. Answer
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