Question

В основании прямой призмы лежит ромб с диагоналями 18 и 24 см. Определите высоту призмы, если площадь её боковой поверхности равна 225 см^ Помогитее!!!

Answer 1

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Answer 2

Calculating the Height of a Prism with a Rhombus Base

To calculate the height of the prism, we can use the formula for the lateral surface area of a prism, which is given by the formula:

Lateral Surface Area = Perimeter of Base * Height

The perimeter of the base of the prism can be calculated using the given diagonals of the rhombus.

Given: - Diagonal 1 (d1) = 18 cm - Diagonal 2 (d2) = 24 cm - Lateral Surface Area = 225 cm^2

Calculating the Perimeter of the Base

The perimeter of the base of the prism (P) can be calculated using the diagonals of the rhombus using the formula:

Perimeter of Rhombus = 2 * (sqrt((d1/2)^2 + (d2/2)^2))

Substitute the given values: - d1 = 18 cm - d2 = 24 cm

Calculating the perimeter of the base: ``` P = 2 * (sqrt((18/2)^2 + (24/2)^2)) ``` ``` P = 2 * (sqrt(81 + 144)) ``` ``` P = 2 * (sqrt(225)) ``` ``` P = 2 * 15 ``` ``` P = 30 cm ```

Calculating the Height of the Prism

Now, we can use the formula for the lateral surface area to calculate the height of the prism:

225 = 30 * Height

Solving for the height: ``` Height = 225 / 30 ``` ``` Height = 7.5 cm ```

The height of the prism is 7.5 cm.