a regular solid has a length of 28cm., a width of 16cm. and a total surface area of 1424cm squared. What is the total surface area of a similar rectangular solid with a length of 14cm.

A = 356 cm²

Explanation:

In this case, you need to use the formula to calculate the area of regular solid.

This is the following expression:

S = 2LH + 2LW + 2WH

Where:

L: length

W: Width

H: Height

But we do not know the height of the solid. We should calculate it with the given data first:

1424 = 2*28*H + 2*28*16 + 2*16*H

1424 = 56H + 896 + 32H

1424 - 896 = 88H

H = 528/88

H = 6 cm

Now that we know the height we can calculate the area of the other solid. In the other solid the length has been reduced to half, so I will assume that the Width and height is also reduced to half.

L2 = 14 cm

W2 = 8 cm

H2 = 3 cm

Replacing we have:

S = (2*14*3) + (2*14*8) + (2*8*3)

S = 356 cm²

And this should be the total surface area, assuming the width and height is reduced to half too.

If you don't assume it's reduced to half, then use the original values of Width and Height. Doing so, the Surface would be:

S = (2*14*6) + (2*14*16) + (2*6*16)

S = 808 cm²