Question

Основа прямої трикутної призми -прямокутний трикутник з катетами 3см і 4см.Висота призми 10см.Знайти площу повної поверхні призми

Answer 1

Применена формула площади полной поверхности прямой призмы

Answer 2

Calculation of the Surface Area of the Prism

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

The right triangular prism has a rectangular base with two legs measuring 3 cm and 4 cm, and a height of 10 cm.

Let's calculate the surface area step by step:

1. Base Area: The base of the prism is a right triangle with legs measuring 3 cm and 4 cm. The area of a triangle is given by the formula: Area = (base * height) / 2. Therefore, the area of the base is:

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

2. Lateral Surface Area: The lateral surface area of a prism is the sum of the areas of its lateral faces. In this case, the prism has three rectangular lateral faces. The area of a rectangle is given by the formula: Area = length * width. The length of each lateral face is equal to the perimeter of the base, which is the sum of all sides. The width of each lateral face is equal to the height of the prism.

The perimeter of the base = 3 cm + 4 cm + 5 cm (hypotenuse of the right triangle) = 12 cm.

Therefore, the lateral surface area = 12 cm * 10 cm = 120 cm².

3. Total Surface Area: The total surface area of the prism is the sum of the base area and the lateral surface area.

Total surface area = Base area + Lateral surface area = 6 cm² + 120 cm² = 126 cm².

Therefore, the total surface area of the given right triangular prism is 126 cm².

Please let me know if you need any further assistance!