The formula to calculate the total yardage needed for a quilt backing is:
\[ Y = \frac{(W + 4) \times (H + 4)}{36} \]
Where:
A quilt backing is the bottom layer of a quilt sandwich, a three-layer packet made up of the quilt top, the batting, and the backing. The backing is typically a large piece of fabric that is used to cover the back of the quilt. It can be a single, unpieced piece of fabric, but it’s also possible to piece together smaller cuts of fabric to create a larger backing. The backing is usually made from a soft, durable material that can withstand repeated use and washing. It’s often a solid color or a simple print so as not to distract from the quilt top, but it can also be a more complex design or even a second quilt top. The backing is attached to the other layers of the quilt sandwich through a process called quilting, where the three layers are sewn together in a decorative pattern.
Let's assume the following values:
Step 1: Add 4 inches to both width and height:
\[ W + 4 = 50 + 4 = 54 \text{ inches} \]
\[ H + 4 = 70 + 4 = 74 \text{ inches} \]
Step 2: Multiply the adjusted width and height:
\[ 54 \times 74 = 3996 \text{ square inches} \]
Step 3: Divide by 36 to convert to yards:
\[ Y = \frac{3996}{36} = 111 \text{ yards} \]
The total yardage needed is 111 yards.
