Question

a. what are the dimensions of each face of the platform?
face a: $3x + 1$ by $x$
face b: $x + 1$ by $x$
face c: $3x + 1$ by $x + 1$
b. what is the area of the top of the platform?
(simplify your answer.)

Explanation:

Step1: Identify top face dimensions

The top face of the platform corresponds to Face C, with dimensions $(3x+1)$ and $(x+1)$.

Step2: Calculate area via FOIL method

Multiply the two binomials:
$$(3x+1)(x+1) = 3x \cdot x + 3x \cdot 1 + 1 \cdot x + 1 \cdot 1$$

Step3: Simplify the expression

Combine like terms:
$$3x^2 + 3x + x + 1 = 3x^2 + 4x + 1$$

Answer:

$3x^2 + 4x + 1$