Question

Основою прямої трикутної призми є прямокутний трикутник із катетати 8 см і 15 см. Висота призми дорівнює 5 см. Обчисліть площу повної поверхні призми. - Помогите решить пожалуйста, срочно.

Answer 1

Всё подробно написала в решении.

Answer 2

Calculation of the Surface Area of a Right Triangular Prism

To calculate the surface area of a right triangular prism, we need to find the areas of its individual faces and then sum them up.

Given: - Base: A right triangle with legs measuring 8 cm and 15 cm. - Height of the prism: 5 cm.

To calculate the surface area, we need to find the areas of the following faces: 1. The two triangular faces (the bases of the prism). 2. The three rectangular faces (the lateral faces of the prism).

Let's calculate the surface area step by step:

Triangular Faces (Bases of the Prism)

The area of a triangle can be calculated using the formula: Area = (base * height) / 2.

In this case, the base of the triangle is 8 cm and the height is 15 cm. Therefore, the area of each triangular face is:

Area of each triangular face = (8 cm * 15 cm) / 2 = 60 cm².

Rectangular Faces (Lateral Faces of the Prism)

The area of a rectangle can be calculated using the formula: Area = length * width.

In this case, the length of each rectangular face is equal to the perimeter of the base triangle, which can be calculated by adding the lengths of its sides. The width of each rectangular face is equal to the height of the prism.

The perimeter of the base triangle is: Perimeter = 8 cm + 15 cm + hypotenuse.

To find the hypotenuse, we can use the Pythagorean theorem: hypotenuse = sqrt(8 cm² + 15 cm²).

Let's calculate the perimeter and the hypotenuse:

Perimeter = 8 cm + 15 cm + sqrt(8 cm² + 15 cm²) = 8 cm + 15 cm + sqrt(64 cm² + 225 cm²) = 8 cm + 15 cm + sqrt(289 cm²) = 8 cm + 15 cm + 17 cm = 40 cm.

Now, let's calculate the area of each rectangular face:

Area of each rectangular face = Perimeter * Height = 40 cm * 5 cm = 200 cm².

Total Surface Area of the Prism

To find the total surface area of the prism, we need to sum up the areas of all the faces:

Total Surface Area = 2 * Area of each triangular face + 3 * Area of each rectangular face.

Substituting the values we calculated earlier:

Total Surface Area = 2 * 60 cm² + 3 * 200 cm² = 120 cm² + 600 cm² = 720 cm².

Therefore, the total surface area of the given right triangular prism is 720 cm².

Please note that the calculations provided above are based on the information given in the question and the formulas for calculating the areas of triangles and rectangles.