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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