Question

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.

Answer 1

The total perimeter of all three figure is 15 x .

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