Question

В прямой треугольной призме стороны основания равны 6см, 8см, 10см, боковое ребро 16см. Найти объем призмы.

Answer 1

Так как в основании призмы лежит прямоугольный треугольник ( т.к. выполняется равенство: $6^{2}+ 8^{2}= 10^{2} \\ 36+64=100$), то площадь основания равна 0,5 * 6 * 8 = 24 (кв.см). Тогда объём призмы : 24 * 16 = 384 (куб.см).

Answer 2

Calculation of the Volume of a Right Triangular Prism

To find the volume of a right triangular prism, we need to multiply the area of the base by the height of the prism. In this case, the base of the prism is a right triangle, and the height is the length of the lateral edge.

Given the following dimensions of the right triangular prism: - Sides of the base: 6 cm, 8 cm, and 10 cm - Lateral edge: 16 cm

We can calculate the volume using the formula:

Volume = (Area of the base) x (Height)

Calculating the Area of the Base

To calculate the area of the base, we can use Heron's formula, which allows us to find the area of a triangle when we know the lengths of its sides.

Heron's formula states that the area of a triangle with sides a, b, and c is given by:

Area = sqrt(s(s-a)(s-b)(s-c))

where s is the semiperimeter of the triangle, calculated as:

s = (a + b + c) / 2

In our case, the sides of the triangle are 6 cm, 8 cm, and 10 cm. Let's calculate the semiperimeter and the area of the base.

Semiperimeter (s) = (6 + 8 + 10) / 2 = 12 cm

Area of the base = sqrt(12(12-6)(12-8)(12-10)) = sqrt(12 * 6 * 4 * 2) = sqrt(576) = 24 cm² .

Calculating the Volume

Now that we have the area of the base (24 cm²) and the height (16 cm), we can calculate the volume of the right triangular prism.

Volume = (Area of the base) x (Height) = 24 cm² x 16 cm = 384 cm³

Therefore, the volume of the given right triangular prism is 384 cm³.

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