Final answer:
Archimedes' result concerning the area of a parabolic segment is a mathematical concept stating that the area is 4/3 of the area of the inscribed triangle. In the context given, the cross-sectional area of a concave mirror, modeled as a quarter-section of a cylinder, is found using A = (2πR)L for calculating the power delivered by solar insolation.
Step-by-step explanation:
The question revolves around finding the area of a parabolic segment in a context that involves physics, but Archimedes' work is primarily mathematical. The correct completion of the sentence would be that according to Archimedes' result, the area of a parabolic segment is 4/3 of the area of the triangle inscribed in it. However, in the context provided, it appears that the student is mixing concepts and is specifically interested in finding the cross-sectional area of a concave mirror to calculate the power delivered by solar insolation. For the quarter-section of a cylinder mirror given, according to the provided information, the cross-sectional area A for a length L of the mirror is given by A = (2πR)L. Hence, for a radius R of 80.0 cm or 0.800 m and length L of 1.00 m, the area A is 1.26 m².