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Part 1
The pair of figures to the right are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number.
Area of smaller parallelogramequals28 ft squared
4 ft
24 ft
To find the area of the larger parallelogram, we need to look at the relationship between their areas according to the similarity of the figures.
The area of similar figures is proportional to the square of the scale factor between them.
In this case, the scale factor can be found by comparing the sides of the two parallelograms. The larger parallelogram is 6 times bigger than the smaller one (24 ft / 4 ft = 6).
Since the scale factor is 6, the area of the larger parallelogram will be 6^2 = 36 times bigger than the area of the smaller parallelogram.
To find the area of the larger parallelogram:
Area of larger parallelogram = 28 ft^2 * 36 = 1008 ft^2
Therefore, the area of the larger parallelogram is approximately 1008 square feet.