Lonna made a quilt for her cousin's doll. The quilt had a 7 × 7 array of different color square patches. If each patch is 1
3
4
in long, what is the area of the whole quilt?
7*7*(7/4)^2 = 4901/16 in^2
2 1/4*2 1/4
To find the area of the quilt, we need to find the total number of square patches in the quilt and then multiply it by the area of each patch.
First, we have a 7 x 7 array of square patches, which means there are 7 patches in each row and 7 patches in each column.
To find the total number of patches in the quilt, we multiply the number of patches in each row (7) by the number of patches in each column (7):
7 patches/row × 7 patches/column = 49 patches
Now that we know there are 49 patches in the quilt, we can find the total area by multiplying this number by the area of each patch.
Each patch is given to be 1 3 4 in long. However, we need to square this value to find the area since the patches are squares.
So, we square the length of each patch: (1 3 4)^2 = 1 3 4 × 1 3 4 = 16 square inches
Finally, we can find the area of the whole quilt by multiplying the total number of patches (49) by the area of each patch (16 square inches):
Area of quilt = 49 patches × 16 square inches/patch = 784 square inches
Therefore, the area of the whole quilt is 784 square inches.
The length of the quilt is 7 x 1 3/4, 1 3/4 as an improper fraction is 7/4
so the length is
7 x 7/4
= 49/4
The area is the lenght times the width (for the square quilt)
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