Question

чему равна площадь полной поверхности правильной четырехугольной пирамиды,ребра основания которой равны 5 см, а апофема 8 см?

Answer 1

S(пол.)=S(осн.)+S(бок.)=25+1/2*P(осн.)*d(апоф.)=25+1/2*8*20=25+80=105

Answer 2

Calculating the Surface Area of a Regular Quadrilateral Pyramid

To calculate the surface area of a regular quadrilateral pyramid, we can use the formula:

Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)

Where: - Base Area = Area of the base of the pyramid - Perimeter of Base = Perimeter of the base of the pyramid - Slant Height = Height of each triangular face of the pyramid

Given Measurements

- Base Edge Length (a) = 5 cm - Apotem (Slant Height) (l) = 8 cm

Calculating the Base Area

The base of a regular quadrilateral pyramid is a square, so the base area can be calculated using the formula for the area of a square:

Base Area = (Side Length)^2

Substituting the given value: Base Area = (5 cm)^2 = 25 cm^2

Calculating the Perimeter of the Base

The perimeter of the base of the pyramid can be calculated by multiplying the edge length by 4 (since it's a square):

Perimeter of Base = 4 * Base Edge Length

Substituting the given value: Perimeter of Base = 4 * 5 cm = 20 cm

Calculating the Surface Area

Now, we can use the formula for the surface area of the pyramid:

Surface Area = 25 cm^2 + (0.5 * 20 cm * 8 cm) Surface Area = 25 cm^2 + 80 cm^2 Surface Area = 105 cm^2

So, the surface area of the regular quadrilateral pyramid with a base edge length of 5 cm and an apotem of 8 cm is 105 cm^2.