Heather has a thin piece of wood that measures 14 inches long by 13 inches wide. She wants to make a box with a height of 3 inches. Heather says that she has enough wood to make a box that has bases measuring 6.5 inches by 6.5 inches. Do you agree?

Yes, I agree. Since the area of the piece of wood is greater than the area of the box she wants to make, then she has enough wood to make the box.

Step-by-step explanation:

First, we will calculate the area of the piece of wood Heather has

Area (A) = Length (l) × Width (w)

From the question, l = 14 inches and w = 13 inches

A = 14 inches × 13 inches

A = 182 squares inches

Hence, the area of the piece of wood is 182 square inches

Now, we will calculate the total surface area of the box she desires to make

Area (A) of a box is given by

A = 2lw + 2lh + 2wh

Where l is the length

w is the width and

h is the height

She wants to make a box with a height of 3 inches and bases measuring 6.5 inches by 6.5 inches.

i.e h = 3 inches, l = 6.5 inches and w = 6.5 inches

∴ A = 2(6.5×6.5) + 2(6.5×3) + 2(6.5×3)

A = 84.5 + 39 + 39

A = 162.5 square inches

Hence, the area of the box she wants to make is 162.5 square inches

Since the area of the piece of wood is greater than the area of the box she wants to make, then she has enough wood to make the box.

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