To solve such problems we need to know about the area of a rhombus.
<h2>Area of a rhombus </h2>
<h2>Given to us
</h2>
- Juan is making a model out of rhombi. Each rhombus will be connected to the one before it.
-
Each Rhombus will be 6 inches tall and 4 inches wide.
<h3>A.) The paper needed for each rhombus </h3>
As it is given that Each Rhombus will be 6 inches tall and 4 inches wide, therefore, the diagonals of the rhombus are 6 inches and 4 inches.
The paper needed for each rhombus = Area of the rhombus
![\begin{aligned}Area\ of\ rhombus &= \dfrac{(Diagonal_1 \times Diagonal_2)}{2}\\&=\dfrac{6 \times 4}{2}\\&= \dfrac{24}{2}\\&= 12\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DArea%5C%20of%5C%20rhombus%20%26%3D%20%5Cdfrac%7B%28Diagonal_1%20%5Ctimes%20Diagonal_2%29%7D%7B2%7D%5C%5C%26%3D%5Cdfrac%7B6%20%5Ctimes%204%7D%7B2%7D%5C%5C%26%3D%20%5Cdfrac%7B24%7D%7B2%7D%5C%5C%26%3D%2012%5Cend%7Baligned%7D)
Therefore, the paper needed for each rhombus is 12 square inches.
<h3>B.) Paper used by Juan</h3>
As it is we have got the area of the rhombus in. We need to change the wall length to the wall to inches.
1 foot = 12 inches
so,
11 feet = 11 x 12 = 132 in
As per the information given each rhombus is 4 inches wide, and we need to cover 132 in. to make the border of the wall. therefore,
![\rm{Number\ of\ rhombus\ needed = \dfrac{Length\ of\ the\ wall}{Width\ of\ the\ rhombus}](https://tex.z-dn.net/?f=%5Crm%7BNumber%5C%20of%5C%20rhombus%5C%20needed%20%3D%20%5Cdfrac%7BLength%5C%20of%5C%20the%5C%20wall%7D%7BWidth%5C%20of%5C%20the%5C%20rhombus%7D)
![=\dfrac{132}{4}\\\\=33](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B132%7D%7B4%7D%5C%5C%5C%5C%3D33)
Thus, a total of 33 rhombus are needed to cover the wall.
<h3>Total paper needed</h3>
![\rm{Total\ paper\ needed = Number\ of\ rhombus\ needed\ \times Area\ of\ rhombus](https://tex.z-dn.net/?f=%5Crm%7BTotal%5C%20paper%5C%20needed%20%3D%20Number%5C%20of%5C%20rhombus%5C%20needed%5C%20%5Ctimes%20Area%5C%20of%5C%20rhombus)
![= 12 in.^2 \times 33\\= 396 in.^2](https://tex.z-dn.net/?f=%3D%2012%20in.%5E2%20%5Ctimes%2033%5C%5C%3D%20396%20in.%5E2)
Therefore, the paper used by Juan is 396 square inches.
Learn more about the area of rhombus:
brainly.com/question/10713731