Question

a quilter created the following shape to use in a block for a new quilt. what is the area of the shape for the quilt block? 63 3/4 in² 112 1/2 in² 127 1/2 in² 225 in²

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\). Here, \(l = 6\) in and \(w = 5\) in. So, \(A_{1}=6\times5 = 30\) \(in^{2}\).

Step2: Calculate the area of the parallelogram

The formula for the area of a parallelogram is \(A = b\times h\). Here, \(b = 13\) in and \(h = 7.5\) in. So, \(A_{2}=13\times7.5=\frac{13\times15}{2}=97.5\) \(in^{2}\).

Step3: Calculate the total area

The total area \(A = A_{1}+A_{2}\). Substitute \(A_{1}=30\) and \(A_{2}=97.5\). Then \(A=30 + 97.5=127.5=127\frac{1}{2}\) \(in^{2}\).

Answer:

\(127\frac{1}{2}\text{ in}^{2}\) (the third option)