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Zorluk: ZorArea of Two-Dimensional Shapes

An aerospace company designs two similar solar panels. The smaller panel is in the shape of a parallelogram and has an area of 8080 square centimeters. If the perimeter of the larger panel is 1.51.5 times the perimeter of the smaller panel, what is the area, in square centimeters, of the larger panel?

  1. A
    120
  2. B
    200
  3. 180Cevap
  4. D
    270

Cevap

180
Since the two solar panels are similar, the ratio of their perimeters is equal to their linear scale factor, k=1.5k = 1.5. The ratio of their areas is equal to the square of the linear scale factor, k2=(1.5)2=2.25k^2 = (1.5)^2 = 2.25. Therefore, the area of the larger panel is the product of the smaller panel's area and the area scale factor: 80×2.25=18080 \times 2.25 = 180 square centimeters.

Adım Adım Çözüm

1
Determine the linear scale factor between the two similar solar panels.
The linear scale factor is k=1.5k = 1.5.
For similar figures, the ratio of any corresponding linear measurements (such as perimeters) is equal to the linear scale factor. Here, the perimeter of the larger panel is 1.51.5 times that of the smaller panel.
2
Calculate the area scale factor by squaring the linear scale factor.
The area scale factor is k2=(1.5)2=2.25k^2 = (1.5)^2 = 2.25.
The ratio of the areas of two similar two-dimensional shapes is equal to the square of their linear scale factor.
3
Multiply the area of the smaller solar panel by the area scale factor to find the area of the larger panel.
The area of the larger solar panel is 80×2.25=18080 \times 2.25 = 180 square centimeters.
Multiplying the original area by the area scale factor yields the scaled area of the larger similar figure.

Anahtar Kavram

Area scaling of similar figures
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Konular

Area of Two-Dimensional Shapes

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