Question

Знайдіть об'єм і площу повної поверхні прямої призми, в основі якої лежить прямокутний трикутник із катетами З см і 4 см, а бічне ребро призми дорівнює 10 см.

Answer 1

Ответ:

Площадь полной поверхности = площади боковой поверхности + 2 площади основания.

1) в оснвоании лежит прямоугольный треугольник. Площадь находим как 1/2 произведения катетов , т..е 12*5:2= 30 см^2/

2)площадь бококвой поверхности = половине периметра основания на высоту.

чтобы найти периметр , надо знать все три стороны треугольника. Треугольник прямоугольный, поэтому гипотенузу находим по теореме Пифагора. 12^2+5^2=144+25=169, гипотенуза равна 13.

3) ищем периметр 13+12+5=30 см.

4) ищем площадь боковой поверхности 30*10=300

5) площадь полной поверхности равна 300+2*30=360 см

Объяснение:

Answer 2

Calculation of the Volume and Surface Area of a Prism

To find the volume and surface area of a prism, we need to know the dimensions of its base and its height. In this case, we have a right triangular base with legs measuring 3 cm and 4 cm, and the prism's lateral edge measures 10 cm.

Finding the Volume of the Prism

The volume of a prism is calculated by multiplying the area of its base by its height. In this case, the base is a right triangle, so we can find its area using the formula:

Area of a right triangle = (base * height) / 2

Given that the legs of the right triangle are 3 cm and 4 cm, the area of the base is:

Area of the base = (3 cm * 4 cm) / 2 = 6 cm²

Now, we can calculate the volume of the prism by multiplying the area of the base by the height:

Volume of the prism = Area of the base * Height

Since the height of the prism is not provided in the question, we cannot calculate the exact volume without that information.

Finding the Surface Area of the Prism

The surface area of a prism is calculated by adding the areas of all its faces. For a right triangular prism, we have three rectangular faces and two triangular faces.

1. The area of the triangular faces can be calculated using the formula:

Area of a triangle = (base * height) / 2

Given that the legs of the right triangle are 3 cm and 4 cm, the area of each triangular face is:

Area of a triangular face = (3 cm * 4 cm) / 2 = 6 cm²

Since there are two triangular faces, the total area of the triangular faces is:

Total area of the triangular faces = 2 * 6 cm² = 12 cm²

2. The area of the rectangular faces can be calculated using the formula:

Area of a rectangle = length * width

Given that the length of the rectangular face is 10 cm and the width is the same as the height of the prism (which is not provided), we cannot calculate the exact area without that information.

Therefore, we can only calculate the area of the triangular faces, which is 12 cm².

Please provide the height of the prism so that we can calculate the exact volume and surface area.