1. consider the right rectangular prism. all lengths shown are in feet.\na. sketch a net of the prism. label…

Brief Explanations:

A net of a right rectangular prism consists of 6 rectangles: 2 pairs of congruent rectangles matching the prism's face dimensions. The prism has dimensions 4 ft, 5 ft, and 8 ft, so the net will include:

• 2 rectangles of 4 ft × 5 ft (top and bottom faces)
• 2 rectangles of 4 ft × 8 ft (front and back faces)
• 2 rectangles of 5 ft × 8 ft (left and right faces) These are arranged connected edge-to-edge to form a flat pattern that folds into the prism.

Answer:

A possible net layout (with labeled lengths):

1. Center rectangle: $4 \text{ ft} \times 8 \text{ ft}$
2. Attach a $4 \text{ ft} \times 5 \text{ ft}$ rectangle to the 4 ft side of the center
3. Attach a $4 \text{ ft} \times 8 \text{ ft}$ rectangle to the opposite 4 ft side of the center
4. Attach a $5 \text{ ft} \times 8 \text{ ft}$ rectangle to one 8 ft side of the center
5. Attach a $5 \text{ ft} \times 8 \text{ ft}$ rectangle to the opposite 8 ft side of the center
6. Attach the remaining $4 \text{ ft} \times 5 \text{ ft}$ rectangle to a free 5 ft edge of one of the side rectangles

(Visual sketch description: A central 4x8 rectangle, flanked by 4x8 and 4x5 rectangles on its 4 ft sides, with 5x8 rectangles on its 8 ft sides, and the final 4x5 rectangle attached to a 5 ft edge of a 5x8 rectangle.)