Question

Боковое ребро правильной четырехугольной пирамиды 10см, а ее высота 8см. Найти площадь боковой поверхности пирамиды

Answer 1

Если пирамида правильная, значит в ее основании лежит правильный четырехугольник т.е квадрат

Sбок=Росн*h=4*10*8=320 кв.см

Sосн=2*а*а=2*10*10=200 кв.см

S=Sбок+Sосн=320+200=520 кв.см 

Answer 2

Calculation of the lateral surface area of a pyramid

To find the lateral surface area of a pyramid, we need to know the length of the lateral edge and the height of the pyramid. In this case, the lateral edge of the pyramid is 10 cm and the height is 8 cm.

The formula to calculate the lateral surface area of a pyramid is:

Lateral Surface Area = (Perimeter of the base) × (Slant height) / 2

The perimeter of the base can be calculated by multiplying the length of one side of the base by the number of sides. Since the pyramid is a four-sided pyramid, the perimeter of the base is 4 times the length of one side.

Let's calculate the lateral surface area of the pyramid step by step:

1. Calculate the perimeter of the base: - The base of the pyramid is a square, so the length of one side of the base is equal to the length of the lateral edge. - The perimeter of the base is 4 times the length of one side: Perimeter of the base = 4 × 10 cm = 40 cm.

2. Calculate the slant height: - The slant height can be found using the Pythagorean theorem, which states that the square of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides. - In this case, the other two sides are half the length of the base (since the base is a square). - Using the Pythagorean theorem, we can calculate the slant height as follows: - Slant height = √((base length/2)^2 + height^2) = √((10 cm/2)^2 + 8 cm^2) = √(25 cm^2 + 64 cm^2) = √(89 cm^2) ≈ 9.43 cm.

3. Calculate the lateral surface area: - Using the formula mentioned earlier, we can calculate the lateral surface area of the pyramid as follows: - Lateral Surface Area = (Perimeter of the base) × (Slant height) / 2 = (40 cm) × (9.43 cm) / 2 ≈ 188.6 cm^2.

Therefore, the lateral surface area of the given pyramid is approximately 188.6 cm^2.