Question

This figure represents a large storage container that will be built out of a new durable material. The storage company needs 8 of these containers.

How much of the new material is needed to build all 8 containers?

Enter your answer in the box.

Answer 1

Answer:

1872 ft.²

Step-by-step explanation:

First lets figure out all of the easy shapes:

The bottom one: 8 * 7 = 56

The one on the left: 5 * 8 = 40

The one of top: 8 * 3 = 24

The slanted rectangle: 5 * 8 = 40

The small rectangle below that : 2 * 8 = 16

Now we just have the polygon facing toward us. It can be broken up into 2 parts:

The lower half: 2 * 7 = 14

Imagine a line going from the top of the line marked "2" straight across to the other side. That is the bottom half. Now we are left with a trapezoid. The formula for the area of a trapezoid is as follows:

A = ((a + b) / 2) * h

What this means is that we had the top and bottom of the figure, divide that by 2, and multiply it by the height. That can be shown here:

(3 + 7) / 2 = 5 * 3 = 15

15 is the area of the trapezoid. Now we can combine that with 14 to get the total area of the polygon:

14 + 15 = 29

Then do the same again for the other identical figure

14 + 15 = 29

Now we have all the areas of our shapes. Let's add them up:

56 + 40 + 24 + 40 + 16 + 29 + 29 = 234

234 is the total surface area of the box. Since there are 8 boxes, multiply this by 8 to get your final answer:

234 * 8 = 1872 ft.²

Don't forget to include units!