Answer:
A = 6x² + 5x + 1
Step-by-step explanation:
The area of a rhombus is \(A= \frac{1}{2} d_{1} d_{2}\) where d₁ is one diagonal and d₂ is the other diagonal.
If we have the rhombus ABCD, the diagonals are AC and BD.
The problem tells us that AC = 3x + 1 and BD = 4x + 2
Substituting this in our formula for the area and simplifying as much as we can (by factorizing) we get:
\(A= \frac{(3x+1)(4x+2)}{2} \\2A= (3x+1)(4x+2)\\2A= 12x^{2} +10x+2\\2A = 2(6x^{2} +5x+1)\\2A=2(3x+1)(2x+1)\\A=(3x+1)(2x+1)\)
Therefore the area is A = (3x + 1) (2x + 1). If you want to solve the parenthesis you'd get A = 6x² + 5x + 1
