Question

meiko is hanging a picture - collage on her wall. the dimensions of the collage are shown in the diagram. she plans to cover the collage with smaller pictures that have the same shape as the collage. if the base of each small picture is 4.5 inches and the height is 3.5 inches, how many small pictures will fit within the collage?
the diagram shows a parallelogram - shaped collage with a base of 18 in, a height of 28 in, and a side length of 32 in. there are multiple - choice options (one of which is 26) below the diagram.

Explanation:

Step1: Calculate the area of the collage

The collage is a parallelogram. The area formula for a parallelogram is \(A = base\times height\). Here, the base \(b = 32\) inches and the height \(h = 28\) inches. So, \(A_{collage}=32\times28 = 896\) square inches.

Step2: Calculate the area of each small picture

Each small picture is also a parallelogram (since they have the same shape as the collage). Using the area formula \(A = base\times height\), with base \(b = 4.5\) inches and height \(h = 3.5\) inches. So, \(A_{small}=4.5\times3.5=\frac{9}{2}\times\frac{7}{2}=\frac{63}{4}=15.75\) square inches.

Step3: Find the number of small pictures

Divide the area of the collage by the area of each small picture. Let \(n\) be the number of small pictures. Then \(n=\frac{A_{collage}}{A_{small}}=\frac{896}{15.75}=\frac{896\times4}{63}=\frac{3584}{63}\approx56.89\). Since we can't have a fraction of a picture, we use the whole - number part.

Answer:

56