a diagram of a toy box is show. its measurements are given in inches. 30 in, 34 in, 40 in.

what is the total surface area of the toy box in square inches.

1 answer

To calculate the total surface area of a rectangular box (like a toy box), you can use the formula:

\[ \text{Surface Area} = 2(lw + lh + wh) \]

where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the box.

From the dimensions provided:

  • Length (l) = 30 inches
  • Width (w) = 34 inches
  • Height (h) = 40 inches

Now, plug in the values into the formula:

  1. Calculate the area of each pair of dimensions:

    • \( lw = 30 \times 34 = 1020 \)
    • \( lh = 30 \times 40 = 1200 \)
    • \( wh = 34 \times 40 = 1360 \)
  2. Now, substitute these values back into the surface area formula: \[ \text{Surface Area} = 2(1020 + 1200 + 1360) \]

  3. Calculate the sum inside the parentheses: \[ 1020 + 1200 + 1360 = 3580 \]

  4. Now multiply by 2: \[ \text{Surface Area} = 2 \times 3580 = 7160 \text{ square inches} \]

Therefore, the total surface area of the toy box is 7160 square inches.