Question

В правильной четырёхугольной пирамиде SABCD точка O - центр основания, S - вершина. SD = 10, SO = 6. Найти площадь боковой, полной поверхности и объём.

Answer 1

Ответ:

160√2:

32(4+5√2)

256

Пошаговое объяснение:

OD najdem, kak katet v prjamougolnom treugolnike, po teoreme Pifagora, gde gipotenuza 10 i drugoj katet 6. Poluchim OD=8. BD=2OD=16.

OD - gipotenuza v prjamougolnom ravnobedrennom treugolnike ABD:

AB=AD. 2AB²=256. AB²=128- eto est plosad osnovanija. AB= 8√2.

Plosad bokovoj poverhnosti: 4 umnozit na 8√2 umnozit na 10 i razdelit na 2. Poluchim 160√2.

Plosad polnoj poverhnosti: 128+160√2=32(4+5√2).

Ovjem piramidi: 128 umnozit na  6 i razdelit na 3=256.

Answer 2

Task: Calculate the Surface Area, Lateral Surface Area, and Volume of a Pyramid

Given: - A right quadrilateral pyramid SABCD with point O as the center of the base, and S as the apex. - SD = 10 - SO = 6

Surface Area of the Pyramid:

The surface area of the pyramid consists of the lateral surface area and the base area. The lateral surface area can be calculated using the slant height and the perimeter of the base, while the base area can be calculated using the base's dimensions.

Lateral Surface Area (A_lateral): The lateral surface area of a pyramid can be calculated using the formula: A_lateral = (1/2) * perimeter of base * slant height

Given that SD = 10 and SO = 6, we need to find the perimeter of the base to calculate the lateral surface area.

Base Area (A_base): The base area of a pyramid with a quadrilateral base can be calculated using the formula for the area of a quadrilateral.

Volume of the Pyramid:

The volume of a pyramid can be calculated using the formula: Volume (V): V = (1/3) * base area * height

Given that the base area and height are required to calculate the volume, we need to find the base area and the height of the pyramid.

Calculations:

1. Lateral Surface Area (A_lateral): - We need to find the perimeter of the base to calculate the lateral surface area.

2. Base Area (A_base): - The base area of a quadrilateral can be calculated using the appropriate formula.

3. Volume (V): - We need to find the base area and the height of the pyramid to calculate the volume.

Let's proceed with the calculations based on the given information and the formulas for the surface area and volume of a pyramid.