3@2

To solve these problems, follow these steps:

31. Найдите диагональ квадрата ABCD.

If the side of the square is \(a\), then the diagonal \(d\) of the square can be found using the formula: \[ d = a\sqrt{2} \]

34. Найдите высоту равностороннего треугольника ABC.

An equilateral triangle has all sides equal. If the side length is \(a\), the height \(h\) can be found using the formula: \[ h = \frac{\sqrt{3}}{2}a \]

35. BC = 16. Найдите площадь ∆ABC.

If the base \(BC = 16\), and given that it is equilateral (all sides equal), the area \(A\) can be calculated using: \[ A = \frac{\sqrt{3}}{4} \times BC^2 \]

37. Найдите площадь ∆ABC.

Given a right triangle, use the formula: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] If \(AC = 4/5\) and \(AB = 45^\circ\), you'll need further context to solve. Assuming standard angles, consider trigonometric relations or further given data.

39. Диагональ прямоугольника равна 8 см. Найдите площадь прямоугольника.

If the diagonal is 8 cm, and \(a\) and \(b\) are the sides of the rectangle, use: \[ a^2 + b^2 = 8^2 = 64 \] If the aspect ratio or either side length is given, solve the system to find both \(a\) and \(b\), then calculate: \[ \text{Area} = a \times b \]

For precise solutions, more information or the specific context of measurements might be needed (e.g., precise side lengths for triangles).