Question

1. a rectangular prism measures 6n (length) by 3m (width) by 3p (height) is cut length wise into three identical pieces. find the surface area gained?

Explanation:

Step1: Identify cut type & new surfaces

Cutting lengthwise into 3 pieces requires 2 cuts. Each cut creates 2 new rectangular faces, so total new faces = $2 \times 2 = 4$.

Step2: Calculate area of one new face

Each new face has dimensions width $\times$ height: $3m \times 3p = 9mp$.

Step3: Compute total gained surface area

Multiply single face area by number of new faces: $4 \times 9mp = 36mp$.

Answer:

$36mp$