The lateral sides of a rectangular trapezoid are 15 and 17 cm, its larger base is 18 cm, calculate

| August 8, 2021 | education

The lateral sides of a rectangular trapezoid are 15 and 17 cm, its larger base is 18 cm, calculate the middle line of the trapezoid

To find the length of the midline, we need to find the second smaller base of the trapezoid. Let us designate this trapezoid as ABCD, AB = 15 cm, CD = 17 cm, base AD = 18 cm. From the top of C to the larger base AD, we lower the height CH = AB. In a right-angled triangle CHD we find the leg HD (according to the Pythagorean theorem):
HD = √ (CD² – CH²) = √ (289 – 225) = √64 = 8 (cm).
Find the smaller base BC:
ВС = AD – HD = 18 – 8 = 10 (cm).
The bases of the trapezoid are known, we find the middle line by the formula:
m = 1/2 * (a + b) = 1/2 * (BC + AD) = 14 (cm).
Answer: The middle line of the trapezoid is 14 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.