Question

quiz 1: surface areas of prisms and pyramids
what is the lateral area of a right prism which has a lateral edge of 4 inches and has a regular pentagonal base with an edge of 12 inches?
188 in²
192 in²
384 in²
240 in²

Explanation:

Step1: Recall Lateral Area Formula

The lateral area \( L \) of a right prism is given by \( L = Ph \), where \( P \) is the perimeter of the base and \( h \) is the lateral edge (height of the prism).

Step2: Calculate Perimeter of Pentagon

A regular pentagon has 5 equal sides. Each side (edge) is 12 inches, so the perimeter \( P = 5 \times 12 = 60 \) inches.

Step3: Substitute into Lateral Area Formula

The lateral edge \( h = 4 \) inches. Using \( L = Ph \), we get \( L = 60 \times 4 = 240 \) square inches.

Answer:

240 in²