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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 parallelogramequals40 ft squared
5 ft
20 ft
To find the area of the larger parallelogram, we can use the properties of similar figures. Since the figures are similar, their corresponding sides are in proportion.
The ratio of corresponding sides of similar figures is the same. Therefore, the ratio of the side lengths of the larger parallelogram to the side lengths of the smaller parallelogram is the same.
In this case, the length of the corresponding sides of the larger parallelogram is 20 ft, while the length of the corresponding sides of the smaller parallelogram is 5 ft.
So, the ratio of the side lengths of the larger parallelogram to the side lengths of the smaller parallelogram is:
20 ft / 5 ft = 4
Since the areas of similar figures are proportional to the square of the scale factor, we can find the area of the larger parallelogram by squaring the scale factor (4) and multiplying it by the area of the smaller parallelogram:
40 ft^2 * 4^2 = 40 ft^2 * 16 = 640 ft^2
Therefore, the area of the larger parallelogram is approximately 640 ft^2.