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Sure, let's solve these problems: 34. **Diagonal of a square ABCD**: - If the side of the square is \( a \), the diagonal \( d \) is given by \( d = a\sqrt{2} \). 35. **Height of an equilateral triangle \(\Delta ABC\)**: - If the side length of the triangle is \( a \), the height \( h \) is given by \( h = \frac{\sqrt{3}}{2}a \). 36. **Area of \(\Delta ABC\) with \( BC = 16\)**: - If the base \( BC \) is 16 and it is an equilateral triangle, the area \( A \) is \( A = \frac{\sqrt{3}}{4} \times 16^2 \). 37. **Area of \(\Delta ABC\)**: - For a right triangle with legs \( a = 4.5 \) and \( b = 6 \), the area \( A \) is \( A = \frac{1}{2} \times a \times b = \frac{1}{2} \times 4.5 \times 6 = 13.5 \). 38. **Area of a rectangle with diagonal 8 cm**: - If the sides are \( x \) and \( y \), and the diagonal is 8, by Pythagoras, \( x^2 + y^2 = 8^2 \). The area is given by \( xy \). - Depending on context, additional information might be needed to find the exact dimensions for maximum area: typically, setting \( x \) and \( y \) equal gives maximum area. Let me know if you need detailed explanations or further assistance!