Question

The figure below is a regular octagon. What fraction of its area is shaded?

• A. 1/3
• B. 1/4
• C. 1/5
• D. 3/8

Answer 1

The correct option is B

1/4

The diagram shows how the octagon can be divided into 4 congruent rectangles and 8 congruent triangles. Let R represent the area of a rectangle and let T represent the area of a triangle. Then the ratio of the shaded region to the area of the entire octagon is $\frac{R+2T}{4R+8T}=\frac{1}{4}$