Figure F shows a gothic window design from the cathedral

Chapter 6, Problem 54

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Figure F shows a gothic window design from the cathedral at Reims, France. (The cathedral was constructed during the years 12111311.) Figure G indicates how the design is formed. Triangle ABC is equilateral and arch ABC is the corresponding equilateral arch. Equilateral triangle GID, congruent to triangle ABC, is constructed such that D is the midpoint of and is parallel to The points E and F are the midpoints of segments and , respectively. The two small arches at the bottom of the figure are equilateral arches corresponding to the equilateral triangles GHE and HIF. For the circle in the figure, the center is D and the radius is AD( ED FD). (a) Let s denote the length of a side in each of the two equilateral triangles ABC and GID. Find the area and the perimeter (in terms of s) of the curved figure AJBCA. Hint: For the area, subtract the area of the semicircle AJB from the area of the equilateral arch ABC. (b) Express (in terms of s) the area and the perimeter of equilateral arch GHE. (c) Show that the area of the curved figure EHF is (d) Express (in terms of s) the perimeter and the area of the curved figure FBI.