Grades 9-10 Video Solutions 2014-Grades 9-10 Video Solutions 2014 problem14

Grades 9-10 Video Solutions 2014 problem14

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Video Summary

The problem involves calculating the area of a regular octagon when given that the shaded area within it is 3 cm². The octagon's area formula is \(2(1+\sqrt{2})S^2\). The shaded area includes two right isosceles triangles and a rectangle. By setting and solving equations using the Pythagorean theorem and other geometric properties, the side length \(S\) and its square are determined. The calculated area for the octagon is 12 cm², concluding the problem with the area represented as answer choice D.

Keywords

regular octagon

area calculation

geometric properties

Pythagorean theorem

shaded area