Question

Боковое ребро и высота правильной пирамиды равны 3√2 и √6. Найти S бок. поверхности.

Answer 1

! Площадь бок. поверхности прав. пирамиды равна произведению половины периметра основания на апофему, т.е.

   S бок= 0,5·Р осн·SM

1)По условию SO=√6,SA=3√2.

   Из Δ АОS-прямоуг.: АО=√АS²-SO²=√(3√2)²-(√6)²=√18-6=√12.

2) Из Δ АВС-правильный: АО- радиус описанной окружности.!Сторона правильного тр-ка равна произведению радиуса описанной окружности на √3, т.е.

  АС=АО·√3=√12·√3=√36=6, тогда Р = 3·6=18.

3) найдём апофему  SM из прям. тр-ка АМS:

SM= √AS²-AM²=√(3√2)²-3²=√18-9=√9=3 .

4)  S бок= 0,5·Р осн·SM= 0,5·18·3=27 (кв.ед.)  

Answer 2

Calculation of the Surface Area of a Pyramid

To find the surface area of a pyramid, we need to know the length of the slant height (l) and the height (h) of the pyramid. In this case, the length of the slant height is given as 3√2 and the height is given as √6.

The formula for the surface area of a pyramid is:

S = 0.5 * l * p + B

Where: - S is the surface area of the pyramid - l is the length of the slant height - p is the perimeter of the base - B is the area of the base

To find the surface area, we need to calculate the perimeter and area of the base.

Calculation of the Perimeter of the Base

Since the pyramid is described as a "regular pyramid," we can assume that the base is a regular polygon. However, the number of sides of the base is not provided in the question. Therefore, we cannot determine the exact shape of the base.

To calculate the perimeter of the base, we need to know the number of sides and the length of each side. Without this information, we cannot calculate the perimeter.

Calculation of the Area of the Base

Similarly, without knowing the exact shape of the base, we cannot calculate the area of the base. The area of the base depends on the shape of the base and the length of its sides.

Therefore, without additional information about the base, we cannot calculate the surface area of the pyramid.

Please provide more details about the base of the pyramid, such as the number of sides and the length of each side, to proceed with the calculation.