Point 13 — Joined 3-D figures

What do we see?

Two prisms joined, or two pyramids joined.

What do we understand?

Equation 1: the surface area for one figure (K = …).
Equation 2: the surface area of the joined figure, i.e. 2K − 2(pasted surface).
Use the second equation to find K, then substitute into the first.

Question 1 of 2

Two identical rectangular prisms each have a height of 90 centimeters (cm). The base of each prism is a square, and the surface area of each prism is K cm². If the prisms are glued together along a square base, the resulting prism has a surface area of $\frac{92}{47}$ K cm². What is the side length, in cm, of each square base?