Subjects geometry

Area Scaling

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Area Scaling


1. **Problem statement:** Find the area of a single triangular petal in the second iteration of the Diamond Symbol of the Daisy Petals figure. 2. **Given:** The base triangle area in the first iteration is $A = \frac{1}{2}bh$. 3. **Scale factor for second iteration:** $k = 2$. 4. **Scaling law for area:** When an object is scaled by factor $k$, area scales by $k^2$: $$A' = k^2 A$$ 5. Substitute values into the formula: $$A' = 2^2 \times \frac{1}{2}bh = 4 \times \frac{1}{2}bh = 2bh$$ 6. **Interpretation:** Each triangular petal in the second iteration has an area of $2bh$, which is four times the initial area of one petal in iteration 1. 7. The table confirms this result: iteration 2 has 16 petals each with area $2bh$, total area $32bh$. **Final answer:** The area of one triangular petal in iteration 2 is $2bh$.