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                     \ 10-Nov-2025  Bharat Arora   Proof-8                                    Reader’s Sign _______________________ Date __________

                    example 1. What is the perimeter of these shapes?

                                 a.                            b.                            c.

                    Solution.  a.                              b.                            c.

                    The perimeter of a polygon is the sum of the lengths of the line segments that enclose
                    the figure.

                    i.e., Perimeter of a polygon = Sum of the lengths of its sides
                    example 2. Find the perimeter of the following shapes. Which shape has the greater

                    perimeter?

                    Solution. Perimeter of shape P  =  Sum of the sides

                                                          =  5 m + 8 m + 10 m + 16 m = 39 m
                                Perimeter of shape Q = Sum of the sides
                                                          =  8 m + 3 m + 5 m + 10 m + 5 m + 2 m + 8 m + 15 m = 56 m
                    Thus, shape Q has the greater perimeter.

                    example 3. The perimeter of a triangle is 26 cm. If the lengths of two sides of the
                    triangle are 8 cm and 12 cm respectively, find the length of its third side.

                    Solution. Let PQR be a triangle such that PQ = 8 cm and QR = 12 cm
                    The perimeter of triangle PQR = PQ + QR + PR
                    Perimeter = 26 cm                                                                            P
                    Sum of two given sides = 8 cm + 12 cm = 20 cm                                         8 cm        ?

                    Length of the third side  = Perimeter – Sum of two sides
                                                 = 26 cm – 20 cm = 6 cm                               Q        12 cm       R

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                                                                                            Perimeter and Area

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