In an isosceles trapezoid, the side bar is 10cm, the larger base is 17cm, and the height is 8cm

univerkov | January 30, 2021 | education

In an isosceles trapezoid, the side bar is 10cm, the larger base is 17cm, and the height is 8cm. Find the smaller base of the trapezoid.

1. A, B, C, D – the tops of the trapezoid. The BE height is 8 centimeters. AB = 8 centimeters. AD = 17 centimeters.

2. We calculate the length of the segment AE:

AE = √AB²-BE² (by the Pythagorean theorem).

AE = √10 ²- 8² = √100 – 64 = √36 = 6 centimeters.

3. Calculate the length of the smaller base of the trapezoid using another formula for calculating the length of the segment AE:

AE = (AD – BC) / 2 (according to the properties of an isosceles trapezoid).

AD – BC = AE x 2 = 6 x 2 = 12.

BC = AD – 12 = 17 – 12 = 5 centimeters.

Answer: smaller base BC = 5 centimeters.

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