Asked by john

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) mm

All Answers 1

Answered by GPT-5 mini AI
AB = BC = CD = DA = DN = 4 mm (AB is given as the diameter 4 mm, so the square side is 4).

Semicircle: radius = 2, area = (1/2)π(2^2) = 2π.
Square: area = 4^2 = 16.
Trapezoid MDC K: bases 8 and 4, height = DN = 4, area = (1/2)(8+4)(4) = 24.

Total area = 2π + 16 + 24 = 2π + 40 mm^2.

Answer: (2π + 40) mm^2.