Question

A long paper strip with a width of 5 cm is folded, as shown in the picture. Find the smallest possible area of the gray triangle that is formed after folding.

Answer 1

By using some logic and the formula of the triangle's area, we will find that the smallest possible area is 12.5 cm²

How to start thinking about the problem.

First of all, for the configuration of this paper strip, we can see that the base of the triangle will always be equal of the width of the paper. Thus, the smallest area will be only dependent of the height of the triangle.

Now, we need to analyze the picture to figure out how we can get the smallest height possible for that triangle.

What is the smallest height possible.

Doing this, we shall see that the smallest height possible is actually when the height equals the width itself, as it's shown in the attached image.

How to calculate the smallest area possible.

Thus, to calculate the smallest area, we just have to use the formula of the area of the triangle, which is   $\frac{b\times h}{2}$, where b is the base and h is the height.

As we previously found, for this question, the

base = height = width of the paper = 5cm

Now, we just have to calculate it with the formula

$Area = \frac{base \times height}{2} \\\\ \\ Area = \frac{5 \times 5}{2} \\ \\ Area = \frac{25}{2}\\ \\ Area = 12.5 cm^{2}$

learn more about the area of the triangle here: brainly.com/question/15442893