The answer is the option A: A. 26.12
The explanation is shown below:
1. As you need the perimeter, you can divide the figure into three triangles (as you can see in the figure attached) to calculate the length of the diagonal lines, which would be the hypotenuses of the triangles.
2. You must apply the Pythagorean Theorem to calculate the hypotenuse of each triangle:
- Red triangle (The legs are 3 and 4):
[tex]h=\sqrt{3^{2}+4^{2}} =5[/tex]
- Blue triangle (The legs are 1 and 2):
[tex]h=\sqrt{1^{2}+2^{2}} =2.23[/tex]
-Green triangle (The legs are 3 and 5):
[tex]h=\sqrt{3^{2}+5^{2}} =5.83[/tex]
3. The figure has is symmetric with respect to the y-axis. So, you can multiply the sum of the hypotenuses obtained by two to calculate the perimeter:
[tex]Perimeter=2(5+2.23+5.83)=26.12[/tex]
