Question

Дан прямой параллелепипед.В основании лежит прямоугольник со сторонами 3и7.Диагональ боковой грани большей стороны=10.Найти площадь боковой поверхности призмы

Answer 1

Прямоугольный треугольник с
 гипотенузой = 10, катет = 7, второй катет = Н ( высота параллелепипеда)
По т. Пифагора:  Н² = 100 - 49 = 51, ⇒ Н = √51
Теперь можно искать  площадь поверхности.  Это 6 попрано равных прямоугольников со сторонами 7 и √51, 7 и 3, √ 51 и 3.
S = 7*√51 *2 + 7*3*2 + √51*3*2 = 14√51 +42 + 6√51 = 20√51 + 42

Answer 2

Calculation of the lateral surface area of the prism

To find the lateral surface area of the given prism, we need to calculate the area of each side and then sum them up.

Given information: - The base of the prism is a rectangle with sides measuring 3 and 7. - The diagonal of one of the lateral faces is 10.

To calculate the lateral surface area, we need to find the height of the prism. Let's denote the height as h.

Using the Pythagorean theorem, we can find the height h:

h = sqrt(10^2 - 3^2) = sqrt(100 - 9) = sqrt(91)

Now that we have the height, we can calculate the lateral surface area of the prism.

The lateral surface area of a rectangular prism is given by the formula:

Lateral Surface Area = 2 * (length * height + width * height)

Substituting the values we have:

Lateral Surface Area = 2 * (3 * sqrt(91) + 7 * sqrt(91))

Simplifying the expression:

Lateral Surface Area = 2 * sqrt(91) * (3 + 7)

Lateral Surface Area = 20 * sqrt(91)

Therefore, the lateral surface area of the given prism is 20 * sqrt(91) square units.