The octagon can be partitioned into five squares and four half squares, each with side length $\sqrt{2}/2$, so its area is \[
\displaystyle\left(5+4 \cdot \frac{1}{2}\right)\left(\frac{\sqrt{2}}{2}\displaystyle\right)^{2}= \boxed{\frac{7}{2}}.
\][asy]
unitsize(2cm);
for (int i=0; i<4; ++i) {
for (int j=0; j<4; ++j) {
draw((i,0)--(i,3),dashed);
draw((0,j)--(3,j),dashed);
};}
draw((1,0)--(2,0)--(3,1)--(3,2)--(2,3)--(1,3)--(0,2)--(0,1)--cycle,linewidth(0.7));
for (int i=0; i<2; ++i) {
label("1",(0.5+2i,2.5),S);
label("1",(0.5+2i,0.5),N);}
label("$\frac{\sqrt{2}}{2}$",(0,1.5),E);
label("$\frac{\sqrt{2}}{2}$",(3,1.5),W);
[/asy]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
An equiangular octagon has four sides of length $1$ and four sides of length $\frac{\sqrt{2}}{2}$, arranged so that no two consecutive sides have the same length. What is the area of the octagon?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{7}{2}
An equiangular octagon has four sides of length $1$ and four sides of length $\frac{\sqrt{2}}{2}$, arranged so that no two consecutive sides have the same length. What is the area of the octagon?
test