109 ¹/₂ in²
Further explanation
Given:
- Rachel made a mosaic from different color rectangle tiles.
- Three tiles measured 3 ¹/₂ inches x 3 inches.
- Six tiles measured 4 inches x 3 ¹/₄ inches.
Question:
What is the area of the whole mosaic in square inches?
The Process:
Let's use the formula of a rectangular area.
[tex]\boxed{\boxed{ \ Area = length \times width \ }}[/tex]
Part-1: three tiles measured 3 ¹/₂ inches x 3 inches.
The area of the three tiles is as follows:
[tex]\boxed{ \ Area = 3 \times length \times width \ }[/tex]
[tex]\boxed{ \ Area = 3 \times 3 \times 3\frac{1}{2} \ }[/tex]
[tex]\boxed{ \ Area = 3 \times 3 \times \frac{7}{2} \ }[/tex]
[tex]\boxed{ \ Area = 9 \times \frac{7}{2} \ }[/tex]
[tex]\boxed{\boxed{ \ Area = \frac{63}{2} \ in^2\ }}[/tex]
Part-2: six tiles measures 4 inches x 3 ¹/₄ inches.
The area of the six tiles is as follows:
[tex]\boxed{ \ Area = 6 \times length \times width \ }[/tex]
[tex]\boxed{ \ Area = 6 \times 4 \times 3\frac{1}{4} \ }[/tex]
[tex]\boxed{ \ Area = 6 \times 4 \times \frac{13}{4} \ }[/tex]
[tex]\boxed{ \ Area = 24 \times \frac{13}{4} \ }[/tex]
Both 24 and 4 are divided by 4.
[tex]\boxed{ \ Area = 6 \times 13 \ }[/tex]
[tex]\boxed{\boxed{ \ Area = 78 \ in^2 \ }}[/tex]
Finally, let's add up the two areas above to get the area of the whole mosaic.
[tex]\boxed{ \ = \frac{63}{2} + 78 \ }[/tex]
[tex]\boxed{ \ = 31\frac{1}{2} + 78 \ }[/tex]
[tex]\boxed{ \ = 109\frac{1}{2} \ }[/tex]
Thus, the area of the whole mosaic is [tex]\boxed{\boxed{ \ = 109\frac{1}{2} \ in^2 \ }}[/tex]
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Keywords: Rachel made a mosaic, different color, rectangle, three tiles, measured, 3 1/2 inches, 3 inches, six tiles, 4 inches x 3 1/4 inches, what is the area, the whole mosaic, in square inches
