Question

lucas built a composite solid by joining 12 identical blocks, with dimensions 4 inches by 5 inches by 7 inches, into three rows of four as shown. what is the total surface area of the composite solid? 1,042 square inches 1,072 square inches 1,992 square inches 521 square inches

Explanation:

Step1: Calculate the new dimensions of the composite solid

• Length: \(4\times7 = 28\) inches (since there are 4 blocks along the length of 7 - inch side)
• Width: \(5\) inches
• Height: \(4\times4=16\) inches (since there are 4 blocks along the height of 4 - inch side)

Step2: Use the surface - area formula for a rectangular prism \(S = 2(lw+lh + wh)\)

• Substitute \(l = 28\), \(w = 5\), and \(h = 16\) into the formula:

$$
LATEXBLOCK0
$$

(Wait, no. Let's re - check the dimension calculation. The correct way:
Since there are 3 rows of 4 blocks.
If the original block has dimensions \(a = 4\) in, \(b = 5\) in, \(c = 7\) in.
The new length \(L=4\times7 = 28\) in (4 blocks along the 7 - in side), the new width \(W = 5\) in, and the new height \(H=3\times4=12\) in (3 blocks along the 4 - in side)

Now use the surface - area formula \(S = 2(lw+lh+wh)\)

$$
LATEXBLOCK1
$$

Answer:

1,072 square inches