The smaller base of the rectangular trapezoid is 9 cm, the large diagonal is 17 cm
| August 11, 2021 | education
The smaller base of the rectangular trapezoid is 9 cm, the large diagonal is 17 cm, and the height is 8 cm. Find the perimeter of the trapezoid.
1. Vertices of the trapezoid A, B, C, D. Angle A – straight line. ВD = 17 cm. Height CE = 8 cm. ВС = 9 cm.
P is the perimeter.
2. Calculate the length of the larger base AD:
AD = √ВD²-AB² (by the Pythagorean theorem).
AB = CE = 8 cm.
AD = √17² – 8² = √289 – 64 = √225 = 15 cm.
3. BC = AE = 9 cm.
4. DE = AD – AE = 15 – 9 = 6 cm.
5. Calculate the length of the side of the CD:
CD = √CE² + DE² = √8² + 6² = √64 + 36 = √100 = 10 cm.
6.R = 10 + 8 + 15 + 9 = 42 cm.
Answer: P = 42 cm.
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