Question

a box is in the shape of an equilateral triangular prism. if the box is to be covered with paper on its lateral sides, how many square inches of paper are needed? 3 in. 8 in. 24 square inches 33 square inches 72 square inches 96 square inches

Explanation:

Step1: Identify lateral face dimensions

Each lateral face is a rectangle with height $3$ in, length $8$ in. The prism has 3 congruent lateral faces (since it's an equilateral triangular prism).

Step2: Calculate area of one face

Area of 1 rectangle: $A_1 = 3 \times 8 = 24$ square inches

Step3: Calculate total lateral surface area

Total area = $3 \times A_1 = 3 \times 24$

Answer:

72 square inches