Question

In the following figure, the regular octagon has a side with a length of $1$. What is the area of the shaded region?

• A. $\sqrt{2}+1$
• B. $\sqrt{2}+2$
• C. $\frac{\sqrt{2}+1}{2}$
• D. $\frac{\sqrt{2}}{2}+1$
• E. $\frac{\sqrt{2}}{2}+2$

Answer 1

The correct option is C $\frac{\sqrt{2}+1}{2}$

Given side length $a=1$
Then Length of medium diagonal which is also the height of the shaded triangle $=a(1+\sqrt{2})=1(1+\sqrt{2})$
Area of the shaded triangle $=\frac{1}{2}\times$ base $\times$ height $=\frac{1}{2}\times 1\times (1+\sqrt{2})=\frac{\sqrt{2}+1}{2}$