Question

applying the area of a rhombus formula
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.
how much paper does he need for each rhombus?
square inches
if his wall is 11 feet long, how much paper does he use?
square inches
132
396
528
792

Explanation:

Step1: Recall area formula for rhombus

The area formula of a rhombus is $A=\frac{1}{2}d_1d_2$, where $d_1$ and $d_2$ are the lengths of the diagonals. Here, the height and width of the rhombus can be considered as the lengths of the diagonals. So $d_1 = 6$ inches and $d_2=4$ inches.

Step2: Calculate area of one rhombus

$A=\frac{1}{2}\times6\times4 = 12$ square - inches.

Step3: Convert wall length to inches

Since 1 foot = 12 inches, a 11 - foot long wall is $11\times12=132$ inches long.

Step4: Determine number of rhombuses

The width of each rhombus is 4 inches. The number of rhombuses that can fit along the 132 - inch long wall is $\frac{132}{4}=33$.

Step5: Calculate total paper area

The total area of paper used is the area of one rhombus times the number of rhombuses. So the total area is $12\times33 = 396$ square inches.

Answer:

For each rhombus: 12 square inches
For the wall: 396 square inches