The base of an isosceles trapezoid is 8cm and 16cm, and the height is 3cm.

The base of an isosceles trapezoid is 8cm and 16cm, and the height is 3cm. Find the perimeter of the trapezoid. the answer should be 34cm.

A trapezoid ABCD is given: AB = CD – lateral sides, AD = 16 cm and BC = 8 cm – bases, BH = 3 cm – height.

1. The smallest segment that the height cuts off from the larger base is equal to the half-difference of the bases, that is:

AH = (AD – BC) / 2 = (16 – 8) / 2 = 8/2 = 4 (cm).

2. Consider △ AHB: ∠AHB = 90 ° (since BH is the height), AH = 4 cm and BH = 3 cm are the legs, AB is the hypotenuse, since it lies opposite the right angle.

By the Pythagorean theorem:

AB = √ (AH² + BH²) = √ (4² + 3²) = √ (16 + 9) = √25 = 5 (cm).

The perimeter of a polygon is equal to the sum of the lengths of all its sides.

The perimeter of the trapezoid ABCD is:

P = AB + BC + CD + AD = 5 + 8 + 5 + 16 = 34 (cm).

Answer: P = 34 cm.




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