The sides of the pentagon are numbered; the first side is 4 cm, and each side is 2 cm

| September 9, 2021 | education

The sides of the pentagon are numbered; the first side is 4 cm, and each side is 2 cm longer than the previous one. Calculate the perimeter of the pentagon.

The lengths of the sides of this pentagon form an arithmetic progression an with the first term a1 equal to 4 cm and the difference of the progression d equal to 2 cm.

Since the perimeter of a pentagon is equal to the sum of the lengths of all sides of this pentagon, to calculate this sum, you can use the formula for the sum of the first n members of the arithmetic progression Sn = (2 * a1 + d * (n – 1)) * n / 2.

Substituting into this formula the values ​​a1 = 4, d = 2 and n = 5, we get:

S5 = (2 * a1 + d * (5 – 1)) * 5/2 = (2 * a1 + d * 4) * 5/2 = 2 * (a1 + d * 2) * 5/2 = (a1 + d * 2) * 5 = (4 + 2 * 2) * 5 = (4 + 4) * 5 = 8 * 5 = 40 cm.

Therefore, the perimeter of this pentagon is 40 cm.

Answer: the perimeter of this pentagon is 40 cm.



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