Question

В правильной треугольной пирамиде боковое ребро равно 4см а сторона основания 6см найти боковую поверхность пирамиды

Answer 1

Sбок= Росн*Н(апофема), значит Росн=3а=18, тк пирамида правильная, апофема делит сторону осн на 2, рассмотрим треугольник, образованный апофемой, по теореме пифагора: апофема^2=а^2-b^2, апофема^2= 16-9, апофема=корень из 7, Sбок= 18корней из 7 см^2

 Ответ: 18 корней из 7 )))

Answer 2

Calculation of the lateral surface area of a right triangular pyramid

To find the lateral surface area of a right triangular pyramid, we need to know the length of the lateral edge and the length of the base.

Given: - Length of the lateral edge (bokovoe rebro) = 4 cm - Length of the base (storona osnovaniya) = 6 cm

To calculate the lateral surface area, we can use the formula:

Lateral Surface Area = (1/2) * Perimeter of the Base * Slant Height

The slant height can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the slant height (h) is the hypotenuse, and the base (6 cm) and the height (unknown) are the other two sides.

Let's calculate the slant height (h) using the Pythagorean theorem:

h^2 = 6^2 + height^2

Simplifying the equation:

h^2 = 36 + height^2

Now, let's substitute the value of the lateral edge (4 cm) into the formula for the perimeter of the base:

Perimeter of the Base = 3 * Length of the Base

Perimeter of the Base = 3 * 6 cm = 18 cm

Now, we can calculate the slant height (h):

h^2 = 36 + height^2

h^2 - height^2 = 36

h^2 = 36 + height^2

h^2 = height^2 + 36

2h^2 = height^2 + 36

h^2 = (height^2 + 36) / 2

h = sqrt((height^2 + 36) / 2)

Now that we have the slant height (h), we can calculate the lateral surface area:

Lateral Surface Area = (1/2) * Perimeter of the Base * Slant Height

Lateral Surface Area = (1/2) * 18 cm * h

Lateral Surface Area = 9 cm * h

Let's calculate the value of the lateral surface area using the given measurements:

Lateral Surface Area = 9 cm * sqrt((height^2 + 36) / 2)

Unfortunately, the given information does not provide the height of the pyramid, so we cannot calculate the exact value of the lateral surface area without that information.

Please provide the height of the pyramid so that we can calculate the lateral surface area accurately.