How to find the perimeter of a rectangular trapezoid if you know its bases (2cm and 8cm) and the large side (10cm)?

univerkov | August 7, 2021 | education

1. The tops of the trapezoid – A, B, C, D. BC = 2 cm. AD = 8 centimeters. CD = 10 centimeters.

∠В = ∠А = 90 °.

2. From vertex C we draw the height CE.

3. Calculate the length of the segment DE:

DE = AD – BC = 8 – 2 = 6 centimeters.

4. We calculate the length of CE:

CE = √СD² – DE² (by the Pythagorean theorem).

CE = √10² – 6² = √100 – 64 = √36 = 6 centimeters.

4. AB = CE = 6 centimeters.

We calculate the perimeter of a given trapezoid:

6 + 10 + 2 + 8 + 26 centimeters.

Answer: The perimeter of the trapezoid is 26 centimeters.

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