The diagonal of the isosceles trapezoid is 41cm. Height 9cm. Find the perimeter of the trapezoid if the side is 15 cm.

1. Vertices of the trapezoid – A, B, C, D. BD – diagonal. AB = CD = 15 cm. HH – height.

2. We calculate the length of the segment AH, which is a leg in a right-angled triangle ABН:

AH = √AB²-BH² = √15²- 9² = √225 – 81 = √144 = 12 cm.

3. Calculate the length of the segment DH, which is a leg in a right-angled triangle BDН:

DН = √ВD² – ВН² = √41²- 9² = √1681 – 81 = √1600 = 40 cm.

2. DH = (AD + BC) / 2.

AD + BC = 2DH = 80 cm.

5.P (perimeter of the trapezoid) = AB + CD + AD + BC = 15 + 15 + 80 = 110 cm.

Answer: P = 110 cm.