Question

abigail wants to make a tapestry in the shape of a parallelogram that is 24 inches across the bottom and 36 inches tall. if she pieces smaller similar parallelograms that are 2 inches at the base and 3 inches tall, how many will she need to make the tapestry?
○ 12
○ 24
○ 144
○ 216

Explanation:

Step1: Calculate the area of the large parallelogram

The area formula for a parallelogram is \(A = base\times height\). For the large parallelogram, \(base = 24\) inches and \(height=36\) inches. So, \(A_{large}=24\times36\).

$$A_{large}=24\times36 = 864$$

Step2: Calculate the area of the small parallelogram

For the small parallelogram, \(base = 2\) inches and \(height = 3\) inches. Using the area formula \(A=base\times height\), we get \(A_{small}=2\times3\).

$$A_{small}=2\times 3=6$$

Step3: Find the number of small parallelograms

Divide the area of the large parallelogram by the area of the small parallelogram. Let \(n\) be the number of small parallelograms. Then \(n=\frac{A_{large}}{A_{small}}\).

$$n=\frac{864}{6}=144$$

Answer:

144