Answer:
592 in.²
Explanation:
The amount of cardboard needed is the total surface area of the prism.
A rectangular prism has 6 faces.
Each pair of opposite faces are congruent.
Place the prism with the length facing you and the width going back on both sides.
There are a bottom face and a top face.
There are a left face and right face.
There are a front face and a back face.
Bottom and top faces:
length = 12 in.
width = 8 in.
area = 12 in. × 8 in. = 96 in.²
total area of bottom and top faces = 2 × 96 in.² = 192 in.²
Left and right faces:
width = 8 in.
height = 10 in.
area = 8 in. × 10 in. = 80 in.²
total area of left and right faces = 2 × 80 in.² = 160 in.²
Front and back faces:
length = 12 in.
height = 10 in.
area = 12 in. × 10 in. = 120 in.²
total area of bottom and top faces = 2 × 120 in.² = 240 in.²
Total surface area = 192 in.² + 160 in.² + 240 in.²
Total surface area = 592 in.²
The entire calculation can be done in 1 step using the surface area formula for a rectangular prism.
SA = 2(LW + LH + WH)
SA = 2(12 in. × 8 in. + 12 in. × 10 in. + 8 in. × 10 in.)
SA = 2(96 in.² + 120 in.² + 80 in.²)
SA = 2(296 in.²)
SA = 592 in.²