Question

Дана правильная четырехунольная пирамида,боковое ребро равно 10см,а сторона основания 12см Найдите апофему и площадь боковой поверхности пирамиды СРОЧНО РЕШИТЕ ПОЖАЛУЙСТА, Т.К. КОНТРОЛЬНАЯ

Answer 1

Правильная 4хугольная пирамида значит в основании квадрат!По условию сторона основания 12см,значит все стороны равны,т.к - квадрат! Апофема падает на середину стороны,а значит делит ее на 2 равные части.Из боковой грани по т.Пифагора найдем апофему:10^2-6^2=64,апофема - 8 см.
Sбок= 1/2*pa, где p — периметр основания правильной пирамиды (ABCDE), a — апофема правильной пирамиды (OS).Sбок=1/2*48*8=192см^2.Если нужен рисунок - пиши!

Answer 2

Еарисуете самостоятельно? боковой треугольник равнобедренный с сторонами 10 и основанием 12. апофема a -и высота и медиана в нем
по т. Пифагора
а^2=10^2-6^2=64
а=8
S бок=р×а/2 где р периметр основания а апофема
р=4×12=48
Sбок=48×8/2=192

Answer 3

Calculation of the Apothem and Surface Area of a Regular Quadrilateral Pyramid

To find the apothem and surface area of a regular quadrilateral pyramid, we need to use the given measurements of the pyramid's lateral edge and the side length of its base.

Given: - Lateral edge (slant height) = 10 cm - Side length of the base = 12 cm

Finding the Apothem:

The apothem of a regular quadrilateral pyramid is the perpendicular distance from the center of the base to the midpoint of any of its sides.

To find the apothem, we can use the Pythagorean theorem. Let's consider a right triangle formed by the apothem, half the side length of the base, and the lateral edge.

Using the Pythagorean theorem, we have:

a^2 + b^2 = c^2

Where: - a = half the side length of the base = 12 cm / 2 = 6 cm - b = apothem (unknown) - c = lateral edge = 10 cm

Substituting the given values into the equation, we can solve for the apothem:

6^2 + b^2 = 10^2

Simplifying the equation:

36 + b^2 = 100

b^2 = 100 - 36

b^2 = 64

Taking the square root of both sides:

b = √64

b = 8 cm

Therefore, the apothem of the pyramid is 8 cm.

Finding the Surface Area of the Pyramid:

The surface area of a regular quadrilateral pyramid can be calculated by finding the sum of the areas of its base and its four triangular faces.

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

Area of the base = (side length)^2

Area of the base = 12 cm * 12 cm = 144 cm^2

The area of each triangular face can be calculated using the formula:

Area of a triangle = (1/2) * base * height

In this case, the base of each triangular face is the side length of the base, which is 12 cm. The height of each triangular face is the apothem, which we found to be 8 cm.

Area of each triangular face = (1/2) * 12 cm * 8 cm = 48 cm^2

Since there are four triangular faces, the total area of the four triangular faces is:

Total area of the four triangular faces = 4 * 48 cm^2 = 192 cm^2

Therefore, the surface area of the pyramid is the sum of the area of the base and the total area of the four triangular faces:

Surface area of the pyramid = Area of the base + Total area of the four triangular faces

Surface area of the pyramid = 144 cm^2 + 192 cm^2 = 336 cm^2

Therefore, the apothem of the pyramid is 8 cm and the surface area of the pyramid is 336 cm^2.

Please note that the calculations provided above are based on the given information and assumptions of a regular quadrilateral pyramid.