Question

Апофема правильной четырехугольной пирамиды равна 19см, а диагональ основания √18см. Найти площадь полной поверхности пирамиды. Помогите пожалуйста срочно

Answer 1

Ответ:

123см²

Объяснение:

D=a√2, где а- сторона квадрата.

а=D/√2=√18/√2=√9=3 см сторона квадрата.

Р=4а=4*3=12см периметр квадрата.

Sбок=1/2*Р*l, где Р- периметр квадрата; l- апофема.

Sбок=1/2*12*19=114 см² площадь боковой поверхности пирамиды.

Sосн=а²=3²=9 см площадь квадрата.

Sпол=Sбок+Sосн=114+9=123 см²

Answer 2

Calculating the Surface Area of a Pyramid

To find the surface area of a pyramid, we can use the formula:

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

Given: - Apothem of the pyramid (a) = 19 cm - Diagonal of the base (√18) = √18 cm

First, let's calculate the base area and the slant height of the pyramid.

Calculating the Base Area

The base area of a square pyramid can be found using the formula:

Base Area = s^2

Where s is the length of one side of the base.

Calculating the Slant Height

The slant height (l) can be found using the formula:

l = √(h^2 + (s/2)^2)

Where h is the height of the pyramid and s is the length of one side of the base.

Solution

Let's calculate the base area and the slant height using the given information.

The diagonal of the base (√18) can be used to find the length of one side of the base: s = √18 / √2 = 3√2 cm

Now, we can calculate the base area: Base Area = (3√2)^2 = 18 cm^2

Next, we can calculate the slant height using the apothem and the length of one side of the base: l = √(19^2 + (3√2 / 2)^2) ≈ 19.36 cm

Calculating the Surface Area

Now that we have the base area and the slant height, we can calculate the surface area of the pyramid using the formula:

Surface Area = 18 + (0.5 * (4 * 3√2) * 19.36) ≈ 18 + (6√2 * 19.36) ≈ 18 + 115.68 ≈ 133.68 cm^2

Therefore, the surface area of the pyramid is approximately 133.68 cm^2.