Answer:
192.7 cm³
Explanation:
You want the volume of a regular pentagonal prism with a base side length of 4 cm and a height of 7 cm.
Base area
The area of a regular n-gon is given by the formula ...
A = n·s²/(4·tan(180°/n))
For n=5 and s=4 cm, the area of the prism base is ...
A = 5·(4 cm)²/(4·tan(36°)) = 20/tan(36°) cm² ≈ 27.528 cm²
Volume
The volume of a prism is ...
V = Bh
where B is the base area, and h is the height. Here, we have h=7 cm, so the volume is ...
V = (27.528 cm²)(7 cm) ≈ 192.7 cm³
The volume of the interior of the box is about 192.7 cm³.