Question

1. Найти площадь боковой и площадь полной поверхности, а также объем прямоугольного параллелепипеда (призмы), если его высота равна 17см, сторона основания 5см, а диагональ основания 13 см.​

Answer 1

S = 17 + 5² + 13 = 55 vot octet

Answer 2

Calculation of the Surface Area, Lateral Surface Area, and Volume of a Rectangular Prism

To find the surface area, lateral surface area, and volume of a rectangular prism (also known as a rectangular parallelepiped), we need to know the height, the length of one side of the base, and the diagonal of the base.

Given: - Height (h) = 17 cm - Length of one side of the base (a) = 5 cm - Diagonal of the base (d) = 13 cm

Surface Area of the Rectangular Prism

The surface area of a rectangular prism is the sum of the areas of all its faces. In this case, the rectangular prism has 6 faces: 2 bases and 4 lateral faces.

The formula to calculate the surface area (A) of a rectangular prism is: A = 2ab + 2bc + 2ac

Where: - a = length of one side of the base - b = width of one side of the base - c = height

In this case, since the base is a rectangle, the width (b) can be calculated using the Pythagorean theorem: b = sqrt(d^2 - a^2)

Let's calculate the surface area:

1. Calculate the width (b): - a = 5 cm - d = 13 cm - b = sqrt(13^2 - 5^2) = sqrt(169 - 25) = sqrt(144) = 12 cm

2. Calculate the surface area (A): - a = 5 cm - b = 12 cm - c = 17 cm - A = 2(5*12) + 2(12*17) + 2(5*17) = 120 + 408 + 170 = 698 cm^2

Therefore, the surface area of the rectangular prism is 698 cm^2.

Lateral Surface Area of the Rectangular Prism

The lateral surface area of a rectangular prism is the sum of the areas of its four lateral faces.

The formula to calculate the lateral surface area (LA) of a rectangular prism is: LA = 2bc + 2ac

Using the values we calculated earlier:

1. Calculate the lateral surface area (LA): - b = 12 cm - c = 17 cm - LA = 2(12*17) + 2(5*17) = 408 + 170 = 578 cm^2

Therefore, the lateral surface area of the rectangular prism is 578 cm^2.

Volume of the Rectangular Prism

The volume of a rectangular prism is the product of the length, width, and height.

The formula to calculate the volume (V) of a rectangular prism is: V = abc

Using the given values:

1. Calculate the volume (V): - a = 5 cm - b = 12 cm - c = 17 cm - V = 5*12*17 = 1020 cm^3

Therefore, the volume of the rectangular prism is 1020 cm^3.

Please let me know if there's anything else I can help you with!