You want to cover a trapezoidal box with paper. You have a sheet of paper that is 1m by 500cm. What is the size box that can be made with minimal wastage? plz plz plz help me with this.. i don't understand how to do this

i don't have any work to show you... i don't get it

To determine the size of the trapezoidal box that can be made with minimal paper wastage, we need to consider the dimensions of the paper and the shape of the box.

Given:
- Sheet of paper: 1m by 500cm

First, let's convert the units for ease of calculation:
1m = 100cm

So, the sheet of paper is 100cm by 500cm.

Now, we need to consider the shape of the trapezoidal box. A trapezoidal box has two parallel bases and four sides, two of which are shorter than the other two.

To minimize the paper wastage, the dimensions of the box should closely match the dimensions of the paper. However, since two of the sides of the box will be shorter, some paper will be wasted.

To find the best dimensions, we need to account for the height, top base, and bottom base of the trapezoidal box.

Let's assume:
- Height of the box: h cm
- Top base of the box: b1 cm
- Bottom base of the box: b2 cm

Now, we need to determine the relationship between the box dimensions and the dimensions of the paper.

1. The height (h) of the box will be the same as the width (100cm) of the paper since the paper will be wrapped around the box.

2. The sum of the lengths of the shorter sides of the trapezoidal box will be equal to the length of the paper (500cm). Therefore, if we subtract the sum of the lengths of the shorter sides from the total length of the paper, we can find the length of the top and bottom bases of the box.

500cm - (b1 + b2) = Length of the longer sides

With this equation, we can determine the dimensions of the box that will result in minimal paper wastage.

For example, let's assume the bottom base (b2) of the box is 50cm. Using the equation above, we can solve for the top base (b1):

500cm - (b1 + 50cm) = Length of the longer sides

Once we know the top base and the height of the box, we can calculate the area of the trapezoidal box.

Area = (b1 + b2) * h / 2

By trying different values for the bottom base (b2) and solving for the top base (b1) using the equation mentioned earlier, we can determine the dimensions of the trapezoidal box that minimizes paper wastage.

Alternatively, you can use a spreadsheet software or programming language to create a program that iterates through different values of b2 and calculates the corresponding b1 and the area of the trapezoidal box. The dimensions that yield the minimum area will be the optimal size for minimal wastage.

I hope this explanation helps you understand how to approach this problem.