Question

В правильной четырехугольной пирамиде стороны основания равны 5см, высота боковой грани равна 7см. Найдите полную поверхность пирамиды. Помогите прошу!!

Answer 1

Пошаговое объяснение:

SABCD - пирамида

АВ=ВС=СD=AD=5 см

SH=7 см

Sполн=?

Sполн=Sосн+Sбок

Sосн=АВ²=5²=25 см²

Sбок=1/2•Росн•SH=1/2•4•AB•7=

=1/2•4•5•7=70 см²

Sполн=25+70=95 см²

ответ: 95 см²

Answer 2

Calculation of the Surface Area of a Pyramid

To find the total surface area of a pyramid, we need to consider the area of the base and the lateral faces.

Given information: - Length of the sides of the base = 5 cm - Height of a lateral face = 7 cm

To calculate the surface area, we need to find the area of the base and the area of each lateral face.

Area of the Base

The base of the pyramid is a square, so the area of the base can be calculated by squaring the length of one side.

Area of the base = (side length)^2

In this case, the side length is 5 cm, so the area of the base is: Area of the base = 5 cm * 5 cm = 25 cm^2.

Area of the Lateral Faces

The lateral faces of the pyramid are triangles. To find the area of each lateral face, we need to calculate the area of one triangle and then multiply it by the number of lateral faces.

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

In this case, the base of the triangle is the side length of the base of the pyramid, which is 5 cm. The height of the triangle is the height of a lateral face, which is 7 cm.

So, the area of one lateral face is: Area of one lateral face = (5 cm * 7 cm) / 2 = 35 cm^2.

Since a pyramid has four lateral faces, the total area of the lateral faces is: Total area of the lateral faces = 4 * 35 cm^2 = 140 cm^2.

Total Surface Area of the Pyramid

To find the total surface area of the pyramid, we need to add the area of the base and the area of the lateral faces.

Total surface area = Area of the base + Total area of the lateral faces

In this case, the area of the base is 25 cm^2 and the total area of the lateral faces is 140 cm^2.

So, the total surface area of the pyramid is: Total surface area = 25 cm^2 + 140 cm^2 = 165 cm^2.

Therefore, the full surface area of the given pyramid is 165 square centimeters.

I hope this helps! Let me know if you have any further questions.