Given a square ABCD with a side of 4 cm. On the side of CD, point E is taken

Given a square ABCD with a side of 4 cm. On the side of CD, point E is taken, such that EA = 5 cm. Find the perimeter of the quadrilateral ABCE.

1. We calculate the length of the segment DE, using the formula of the Pythagorean theorem:

DE = √AE² – AD² = √5² – 4² = √25 – 16 = √9 = 3 centimeters.

2. CE = SD – DE = 4 – 3 = 1 centimeter.

3. The total length of the sides of the quadrilateral ABCE (perimeter) = AB + BC + CE + AE = 4 + 4 + 1 + 5 = 14 centimeters.

Answer: The perimeter of the ABCE quadrilateral is 14 centimeters.