Grades 11-12 Video Solutions 2010-11&12 Video Solutions 2010 problem12

11&12 Video Solutions 2010 problem12

Video Transcription

Video Summary

The square has a side length of 2, and the shaded circles are centered at the midpoints of the sides. The goal is to find the sum of the areas of these circles. By using the Pythagorean theorem, the radius of the larger arc (capital R) is determined to be the square root of 2. The smaller circle's radius (little r) is calculated as the square root of 2 minus 1. The area of one circle is π(r²), and with four circles, the total area is four times π(root 2 - 1)², which corresponds to choice A in the problem's options.

Keywords

square

circles

Pythagorean theorem

radius

area