Answer:
8. 24 cm²
9. 72 cm²
10. 20k²
Explanation:
Let's come up with a rule, then we will solve all problems.
We start by answering this question.
If the area of one figure is enlarged by a scale factor of k to get to a second figure, by what factor does the area of the second figure change?
There are two figures with a scale factor of k.
For example, there is a square with side s.
Then there is a second square which is enlarged by a factor of k, k > 1.
The side of the enlarged square is ks.
area of square = (side)²
The area of the smaller square is s².
The area of the larger square is (ks)² = k²s².
scale factor from old to new = (new length) / (old length)
The scale factor is ks/s = k
The ratio of the areas is k²s²/s² = k²
From here we see that if the side is enlarged by a factor of k, then the area is enlarged by a factor of k².
The area is enlarged by the square of the scale factor. To find the new area, multiply the old area by the square of the scale factor.
Now we solve problems 8, 9, 10.
Question 8:
original area = 6 cm²
scale factor = 2 = k
factor of the area = k² = 2² = 4
enlarged area = 6 cm² × 4 = 24 cm²
Question 9:
original area = 8 cm²
scale factor = 3 = k
factor of the area = k² = 3² = 9
enlarged area = 8 cm² × 9 = 72 cm²
Question 10.
original area = 20 cm²
scale factor = k
factor of the area = k²
enlarged area = 20 cm² × k² = 20k² cm²