I have a math question. Know the answer?

Question

Clarissa is building a custom dining room table. The center of it is a rectangular section made from polished slate. The section measures 36 inches by 64 inches. She is also going to place a flat wooden surface of 8 inches all the way around the above section. What is the surface area of the wood used?

Answer 1

1856 square inches.

Answer 2

picture the 8 inch wide wood ring around the table. It adds 8 inches to the front, the back, the left and the right. so now the whole table dimension is 52 by 80 (add 16 to length, 16 to width)

area of slate = 36 x 64 = 2304

area with wood added = 52 x 80 = 4160

so the wood area is the difference of 1856

you can also mentally calculate this like a carpenter building it:

I lay a strip of wood to the right and left, these are length, they each are 8x80 = 640, there's two of them so area is 1280

now two more strips for the short ends that sit IN-BETWEEN the sticking out portions of the long strips, so 36 x 8 = 288, times two is 576.

1280 +576 = 1856, and you see you did it a little differently this time, but the answer is the same.