Questions: In Exercises 19-22, the polygons are similar. The area one polygon is given. Find the area of the other polygon (See Example 5.) 19. 6 ft 20. A=10 cm^2

In Exercises 19-22, the polygons are similar. The area one polygon is given. Find the area of the other polygon (See Example 5.) 19. 6 ft 20. A=10 cm^2
Transcript text: In Exercises 19-22, the polygons are similar. The area one polygon is given. Find the area of the other polygon (See Example 5.) 19. \[ 6 \mathrm{ft} \] 20. \[ A=10 \mathrm{~cm}^{2} \]
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Solution

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Solution Steps

Step 1: Find the scale factor for the rectangles.

The ratio of corresponding sides is 6 ft / 3 ft = 2. The scale factor is 2.

Step 2: Find the area of the larger rectangle.

The ratio of the areas of similar figures is the square of the scale factor. So the area of the larger rectangle is 2² * 27 ft² = 4 * 27 ft² = 108 ft².

Step 3: Find the scale factor for the triangles.

The ratio of corresponding sides is 12 cm / 4 cm = 3. The scale factor is 3.

Step 4: Find the area of the larger triangle.

The ratio of the areas of similar figures is the square of the scale factor. So the area of the larger triangle is 3² * 10 cm² = 9 * 10 cm² = 90 cm²

Step 5: Find the scale factor for the rectangles.

The ratio of corresponding sides is 20 in / 4 in = 5. The scale factor is 5.

Step 6: Find the area of the larger rectangle.

We are not given the area of the smaller rectangle. But from step 5, we can find the area of the larger rectangle given the area of the smaller one, by multiplying by the square of the scale factor which is 5^2=25.

Final Answer

  1. 108 ft²
  2. 90 cm²
  3. 25 times the area of the smaller rectangle
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