Question

Основанием прямой призмы является прямоугольный треугольник со сторонами 4,5 см; 10,8 см; 11,7 см. Высота призмы равна 6 см. Найди площадь полной поверхности и объем призмы. СРОЧНОО

Answer 1

Объем уверен, а площадь полной поверхности не очень

Answer 2

#### Given Information We are given that the base of the prism is a right triangle with sides measuring 4.5 cm, 10.8 cm, and 11.7 cm. The height of the prism is 6 cm. We need to find the total surface area and volume of the prism. #### Calculating the Total Surface Area To calculate the total surface area of the prism, we need to find the areas of the three rectangular faces and the two triangular faces. The area of a rectangle is given by the formula: **Area = length × width**. The area of a triangle is given by the formula: **Area = (base × height) / 2**. Let's calculate the areas of the faces: 1. Area of the rectangular face with dimensions 4.5 cm and 10.8 cm: **Area1 = 4.5 cm × 10.8 cm**. 2. Area of the rectangular face with dimensions 4.5 cm and 11.7 cm: **Area2 = 4.5 cm × 11.7 cm**. 3. Area of the rectangular face with dimensions 10.8 cm and 11.7 cm: **Area3 = 10.8 cm × 11.7 cm**. 4. Area of the triangular face with base 4.5 cm and height 6 cm: **Area4 = (4.5 cm × 6 cm) / 2**. 5. Area of the triangular face with base 10.8 cm and height 6 cm: **Area5 = (10.8 cm × 6 cm) / 2**. Now, let's calculate the total surface area by summing up the areas of all the faces: **Total Surface Area = Area1 + Area2 + Area3 + Area4 + Area5**. #### Calculating the Volume To calculate the volume of the prism, we need to find the area of the base and multiply it by the height. The area of the base, which is a right triangle, can be calculated using the formula: **Area = (base × height) / 2**. Let's calculate the area of the base using the dimensions provided: **Base Area = (4.5 cm × 10.8 cm) / 2**. Now, we can calculate the volume of the prism by multiplying the base area by the height: **Volume = Base Area × Height**. #### Calculation Let's calculate the total surface area and volume of the prism using the given dimensions: 1. Area1 = 4.5 cm × 10.8 cm = 48.6 cm². 2. Area2 = 4.5 cm × 11.7 cm = 52.65 cm². 3. Area3 = 10.8 cm × 11.7 cm = 126.36 cm². 4. Area4 = (4.5 cm × 6 cm) / 2 = 13.5 cm². 5. Area5 = (10.8 cm × 6 cm) / 2 = 32.4 cm². Total Surface Area = Area1 + Area2 + Area3 + Area4 + Area5 = 48.6 cm² + 52.65 cm² + 126.36 cm² + 13.5 cm² + 32.4 cm² = 273.51 cm². Base Area = (4.5 cm × 10.8 cm) / 2 = 24.3 cm². Volume = Base Area × Height = 24.3 cm² × 6 cm = 145.8 cm³. Therefore, the total surface area of the prism is **273.51 cm²** and the volume of the prism is **145.8 cm³**. Please note that the calculations provided above are based on the given dimensions and formulas.