Question

which diagram is a net for this prism?what is the surface area of the triangular prism?$square$ square inches

Explanation:

Step1: Identify prism components

The prism has 2 congruent triangular bases (base = 24 in, height = 5 in) and 3 rectangular faces with dimensions: 24×10, 13×10, 13×10.

Step2: Calculate area of triangular bases

Area of 1 triangle: $\frac{1}{2} \times 24 \times 5 = 60$
Total for 2 triangles: $2 \times 60 = 120$

Step3: Calculate area of rectangles

Area of 24×10 rectangle: $24 \times 10 = 240$
Area of each 13×10 rectangle: $13 \times 10 = 130$
Total for 2 rectangles: $2 \times 130 = 260$

Step4: Sum all areas

Total surface area: $120 + 240 + 260$

The correct net is the left diagram. It has 2 congruent triangular bases (with base 24 in, height 5 in) attached to the 24-in side of the middle 24×10 rectangle, plus the two 13×10 rectangles attached to the 10-in sides of the middle rectangle, matching the dimensions of the original prism.

Answer:

620 square inches