Question

a cardboard carrying box has the dimensions shown below. how many square inches of cardboard are needed to make the box?

Explanation:

Step1: Identify box components

The box has a rectangular base (6×10×5), two triangular ends, and two rectangular roof panels.

Step2: Calculate base area

Base area: $2×(6×5 + 10×5 + 6×10) - 2×(6×5)$ (subtract top face replaced by roof)
$= 2×(30 + 50 + 60) - 60 = 280 - 60 = 220$ sq in

Step3: Calculate triangular ends area

Each triangle: $\frac{1}{2}×6×4$, two triangles: $2×(\frac{1}{2}×6×4) = 24$ sq in

Step4: Calculate roof panels area

Each roof panel: $10×5$, two panels: $2×(10×5) = 100$ sq in

Step5: Total cardboard area

Sum all parts: $220 + 24 + 100 = 344$ sq in

Answer:

344 square inches