Question

Дано: призма Основанием прямой треугольной призмы является прямоугольный треугольник с катетами а=6 см и в=8 см Н=7 см Найти: S пол. повер-? V-?

Answer 1

Ответ:

площадь треугольника= 1/2а*h =1/2*8*6= 24 см2 основание призмы

V=Sосн.*h=24*7= 168 см3

Sпол.пов.= Росн*h= 24*7*2=336 см2

гипотенуза= корень квадратный из (36+64)=10 см

периметр основаня равен:6+8+10= 24 см

Пошаговое объяснение:

Answer 2

Calculation of Surface Area (S) of the Prism:

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

The prism has two triangular faces and three rectangular faces.

1. Triangular Faces: - The base of the prism is a right-angled triangle with legs (or catheti) a = 6 cm and b = 8 cm. - The area of a triangle can be calculated using the formula: Area = (1/2) * base * height. - In this case, the base is a = 6 cm and the height is h = 7 cm (given). - Therefore, the area of one triangular face is: (1/2) * 6 cm * 7 cm = 21 cm².

2. Rectangular Faces: - The prism has three rectangular faces. - The dimensions of these faces are: - Face 1: Length = 6 cm, Width = 8 cm. - Face 2: Length = 6 cm, Width = 7 cm. - Face 3: Length = 8 cm, Width = 7 cm. - The area of a rectangle can be calculated using the formula: Area = length * width. - Therefore, the areas of the three rectangular faces are: - Face 1: 6 cm * 8 cm = 48 cm². - Face 2: 6 cm * 7 cm = 42 cm². - Face 3: 8 cm * 7 cm = 56 cm².

To find the total surface area (S) of the prism, we sum up the areas of all the faces: S = 2 * (Area of triangular face) + 3 * (Area of rectangular face).

Substituting the values we calculated: S = 2 * 21 cm² + 3 * (48 cm² + 42 cm² + 56 cm²).

Calculating the values: S = 42 cm² + 3 * 146 cm².

Simplifying the expression: S = 42 cm² + 438 cm².

Calculating the sum: S = 480 cm².

Therefore, the surface area of the given prism is 480 cm².

Calculation of Volume (V) of the Prism:

To find the volume of the given prism, we need to calculate the area of the base and multiply it by the height.

The base of the prism is a right-angled triangle with legs (or catheti) a = 6 cm and b = 8 cm. The area of a triangle can be calculated using the formula: Area = (1/2) * base * height.

In this case, the base is a = 6 cm and the height is h = 7 cm (given). Therefore, the area of the base is: (1/2) * 6 cm * 7 cm = 21 cm².

To find the volume (V) of the prism, we multiply the area of the base by the height: V = Area of base * height.

Substituting the values we calculated: V = 21 cm² * 7 cm.

Calculating the value: V = 147 cm³.

Therefore, the volume of the given prism is 147 cm³.

Please note that the calculations provided are based on the given dimensions and formulas for calculating the surface area and volume of a prism.