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d1i1m1o1n [39]
3 years ago
8

How to find the area of a regular polygon?

Mathematics
2 answers:
vaieri [72.5K]3 years ago
4 0
To find the regular follow this formula ; area = 1/2 x perimeter x apothem. Which means ... perimeter = the sum of lengths of the all sides
olchik [2.2K]3 years ago
4 0
To find the area of a regular polygon, we need to use the formula A = (1/2)(apothem)(perimeter). The apothem is the radius of the polygon.
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A square in a rectangle have the same perimeter. The length of a side of the square is 4x-1. The length of the rectangle is 2x+2
Thepotemich [5.8K]

The value x is 1, if the perimeter of square and rectangle are same. The perimeter of square and rectangle is 12 units.

Step-by-step explanation:

The given is,

                A square in a rectangle have the same perimeter

                The length of a side of the square is 4x-1

                The length of the rectangle is 2x+2 and width is 2x

Step:1

                Let, a - Side of square

                        l - Length of the rectangle

                       w - Width of the rectangle

Step:2

                Formula for perimeter of square is,

                                    p=4a.............................(1)

                Formula for perimeter of rectangle is,

                                   p=2(l+w)....................(2)

Step:3

                From given,

                            Equation (1) = Equation (2)

                                 4a = 2 (l+w)

               where,

                         a = 4x-1

                          l = 2x+2

                         w = 2x

               Substitute the values,

                       4 ( 4x-1 ) = 2 ( 2x+2+2x )

                            16x - 4 = 2 (4x + 2)

                            16x - 4 = 8x + 4

                          16x - 8x = 8                      

                                   8x = 8

                                     x = 1

Step:4

         Substitute the values of x,

                   a = 4(1)-1 = 3

                     l = 2(1)+2) = 4

                   w = 2(1) = 2

          Perimeter of square and rectangle is 12 units

Result:

           The value x is 1, if the perimeter of square and rectangle are same. The perimeter of square and rectangle is 12 units.

5 0
2 years ago
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