To find the total surface area of a rectangular box (or cuboid), we 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.
Given the dimensions:
- \(L = 34\) inches,
- \(W = 40\) inches,
- \(H = 30\) inches.
Now, we can calculate the surface area step by step.
-
Calculate the area of each pair of opposite faces:
- \(LW = 34 \times 40\)
- \(LH = 34 \times 30\)
- \(WH = 40 \times 30\)
-
Calculate each area:
- \(LW = 34 \times 40 = 1360\) square inches
- \(LH = 34 \times 30 = 1020\) square inches
- \(WH = 40 \times 30 = 1200\) square inches
-
Sum these areas:
- \(LW + LH + WH = 1360 + 1020 + 1200\)
Performing the addition:
- \(1360 + 1020 = 2380\)
- \(2380 + 1200 = 3580\)
-
Multiply the sum by 2 to find the total surface area:
- \(\text{Surface Area} = 2 \times 3580 = 7160\) square inches
So, the total surface area of the toy box is:
\[ \boxed{7160} \text{ square inches} \]
1 answer