A,A,A,A, - straight prism. Find: 1) the lateral surface area of the prism; 2) the total surface area of the prism.

Задание (на английском)

Given: Straight prism A₁A₂A₃A₄.

Find: 1) Lateral surface area (S_бок); 2) Total surface area (S_полн).

Solution:

This problem statement is incomplete as it does not specify the shape of the base or its dimensions. To solve this, we need to make assumptions based on the visual representation (though not provided here in full context) or typical geometry problems. Assuming the base is a rectangle with sides 5 and 3, and the height is 4 (as might be inferred from similar problems):

1. Lateral Surface Area (S_бок):

   The lateral surface area is the perimeter of the base multiplied by the height of the prism.

   \[ S_{бок} = P_{base} \times h \]

   Assuming the base is a rectangle with sides 5 and 3:

   \[ P_{base} = 2 \times (length + width) = 2 \times (5 + 3) = 2 \times 8 = 16 \]

   Assuming the height (h) is 4:

   \[ S_{бок} = 16 \times 4 = 64 \]

2. Total Surface Area (S_полн):

   The total surface area is the lateral surface area plus the area of the two bases.

   \[ S_{полн} = S_{бок} + 2 \times S_{base} \]

   Area of the base (rectangle):

   \[ S_{base} = length \times width = 5 \times 3 = 15 \]

   Total surface area:

   \[ S_{полн} = 64 + 2 \times 15 = 64 + 30 = 94 \]

Answer: 1) S_бок = 64; 2) S_полн = 94