Isosceles trapezoid, lateral side 15 cm, height 12 cm, midline 40 cm. Find the base of the trapezoid.

| August 3, 2021 | education

1. The tops of the trapezoid A, B, C, D. AB = CD = 15 centimeters. Height BE = 12 centimeters. MK is the middle line.

2. Calculate the length of the segment AE. In a right-angled triangle ABE, it is a leg. For the calculation, we use the Pythagorean theorem:

AE = √AB² – BE² = √15² – 12² = √225 – 144 = √81 = 9 centimeters.

3. We calculate the total length of the bases of the trapezoid. To do this, we use the formula for calculating the middle line of a trapezoid:

MK = (BC + AD) / 2 = 40.

BC + AD = 80 centimeters.

4. We calculate the difference in the lengths of the bases. To do this, we use the formula for calculating the length of the smaller of the segments (AE), into which the height BE is divided by the base AD:

AE = (AD – BC) / 2 = 9.

AD – BC = 18 centimeters.

5. Add the expressions from points 3 and 4:

BC + AD + AD – BC = 98.

2AD = 98.

AD = 49 centimeters.

BC = 80 – 49 = 31 centimeters.

Answer: the base of the trapezoid AD = 49 centimeters. BC = 31 centimeters.



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