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A trapezoid, square, and semicircle are connected to form a composite figure. Trapezoid M D C K has base lengths of 8 millimeters and 4 millimeters. Square A B C D has side lengths of 2 millimeters. Line A B is the diameter of the semicircle and has a length of 4 millimeters.
What is the area of the composite figure if AB ≅ BC ≅ CD ≅ DA ≅ DN?
(2π + 28) mm2
(2π + 32) mm2
(2π + 40) mm2
(2π + 48) mm2
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GPT-5 mini
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Answer: (2π + 40) mm².
Reason: AB is the diameter of the semicircle and AB = BC = CD = DA = DN, so each of those segments equals 4 mm. Thus the square ABCD has side 4 (area 4^2 = 16), the semicircle has radius 2 so its area is (1/2)π(2^2) = 2π, and the trapezoid with bases 8 and 4 and height DN = 4 has area (1/2)(8+4)(4) = 24. Total area = 16 + 24 + 2π = 40 + 2π.
Reason: AB is the diameter of the semicircle and AB = BC = CD = DA = DN, so each of those segments equals 4 mm. Thus the square ABCD has side 4 (area 4^2 = 16), the semicircle has radius 2 so its area is (1/2)π(2^2) = 2π, and the trapezoid with bases 8 and 4 and height DN = 4 has area (1/2)(8+4)(4) = 24. Total area = 16 + 24 + 2π = 40 + 2π.
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