1. **State the problem:** We have two similar shapes, C and D. Shape C has perimeter 180 mm and area 1332 mm^2. Shape D has perimeter 300 mm. We need to find the area of shape D. 2. **Recall the properties of similar shapes:** - The ratio of perimeters equals the scale factor $k$. - The ratio of areas equals the square of the scale factor $k^2$. 3. **Calculate the scale factor $k$ for the perimeters:** $$k = \frac{\text{Perimeter of D}}{\text{Perimeter of C}} = \frac{300}{180} = \frac{5}{3}$$ 4. **Calculate the area of shape D using the scale factor:** $$\text{Area of D} = \text{Area of C} \times k^2 = 1332 \times \left(\frac{5}{3}\right)^2$$ 5. **Simplify the expression:** $$\left(\frac{5}{3}\right)^2 = \frac{25}{9}$$ 6. **Calculate the area:** $$\text{Area of D} = 1332 \times \frac{25}{9}$$ 7. **Simplify the multiplication:** $$1332 \times \frac{25}{9} = \frac{1332 \times 25}{9}$$ 8. **Divide 1332 by 9:** $$\frac{1332}{9} = \cancel{\frac{1332}{9}} = 148$$ 9. **Multiply 148 by 25:** $$148 \times 25 = 3700$$ 10. **Final answer:** The area of shape D is **3700 mm\textsuperscript{2}**.