The perimeter of the pentagon is 30 cm, find its area if the length of one of the sides is 6 cm.

1) Find the length of the second side of the rectangle.
The perimeter of a rectangle is the sum of the length and width of the rectangle multiplied by 2. Let’s write the formula for the perimeter of a rectangle:
P = (a + b) × 2,
where a and b are the lengths of the sides of the rectangle. We are given one of the sides of the rectangle. Let us be given side a.
Let us express side b from the formula for the perimeter:
P = 2 a + 2 b,
2 b = P – 2 a,
b = (P – 2 a): 2.
Find the length of the side b of the rectangle by substituting the length of the side a and the perimeter into the formula:
b = (30 – 2 × 6): 2 = (30 – 12): 2 = 18: 2 = 9 cm.
2) Find the area of ​​the rectangle.
The area of ​​a rectangle is the product of the lengths of its sides. Let’s write the formula for the area:
S = a × b,
where a and b are the lengths of the sides of the rectangle.
Find the area of ​​a rectangle by substituting the lengths of its sides into the formula:
S = 6 × 9 = 54 cm².
Answer: the area of ​​the rectangle is 54 cm².