Question

Найдите площадь поверхности правильной четырехугольной пирамиды,стороны основания которой равны 8 и высота равна 3

Answer 1

Ищем апофему по формуле  f=корень (h^2+a^2/4)=корень(3^2+8^2/4)=5

дальше площадь боковой грани Sбок= 1/2а*f=1/2*8*5=20

площадь боковой поверхности правильной четырехугольной пирамиды Sбок.п=4Sбок=20*4=80

площадь основания S0=a^2=8^2=64

площадь поверхности правильной четырехугольной пирамиды S=S0+4*Sбок =64+80=144

Ответ: 144

 

 

Answer 2

Calculation of the Surface Area of a Regular Quadrilateral Pyramid

To find the surface area of a regular quadrilateral pyramid, we need to know the length of the base sides and the height of the pyramid. In this case, the length of the base sides is given as 8 units, and the height is given as 3 units.

The formula to calculate the surface area of a regular quadrilateral pyramid is:

Surface Area = Base Area + Lateral Area

1. Base Area: - The base of the pyramid is a regular quadrilateral, which means all sides are equal in length. - The formula to calculate the area of a regular quadrilateral is: Area = (s^2) * (sqrt(3)/4), where s is the length of the side. - Substituting the given value of the side length (s = 8) into the formula, we can calculate the base area.

2. Lateral Area: - The lateral area of a pyramid is the sum of the areas of the triangular faces. - Since the pyramid is regular, all the triangular faces are congruent. - The formula to calculate the area of a triangle is: Area = (1/2) * base * height, where the base is the length of the side of the base quadrilateral, and the height is the height of the pyramid. - Substituting the given values of the base side length (8) and the height (3) into the formula, we can calculate the area of one triangular face. - Since there are four triangular faces, we multiply the area of one face by 4 to get the total lateral area.

Let's calculate the surface area of the given regular quadrilateral pyramid using the provided values.

Calculation:

1. Base Area: - Using the formula for the area of a regular quadrilateral, with a side length of 8 units: - Base Area = (8^2) * (sqrt(3)/4) = 64 * (sqrt(3)/4) = 16 * sqrt(3) square units.

2. Lateral Area: - Using the formula for the area of a triangle, with a base length of 8 units and a height of 3 units: - Area of one triangular face = (1/2) * 8 * 3 = 12 square units. - Since there are four triangular faces, the total lateral area is: Lateral Area = 4 * 12 = 48 square units.

3. Surface Area: - The surface area of the regular quadrilateral pyramid is the sum of the base area and the lateral area: - Surface Area = Base Area + Lateral Area = 16 * sqrt(3) + 48 square units.

Therefore, the surface area of the given regular quadrilateral pyramid, with base sides of length 8 units and a height of 3 units, is 16 * sqrt(3) + 48 square units.