Question

в правильной четырехугольной пирамиде сторона основпния 10,высота 12,найти площадь боковой поверхности пирамиды

Answer 1

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 base side and the height of the pyramid. In this case, the length of the base side is given as 10 and the height is given as 12.

The formula for the lateral surface area of a pyramid is:

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

To calculate the perimeter of the base, we need to know the number of sides of the base and the length of each side. Since the pyramid is described as a "four-sided pyramid," we can assume it has a square base.

The perimeter of a square is calculated by multiplying the length of one side by 4. In this case, the length of one side is given as 10, so the perimeter of the base is 10 x 4 = 40.

Now, we need to find the slant height of the pyramid. The slant height is the height of each triangular face of the pyramid. To calculate the slant height, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In our case, the height of the pyramid is given as 12, and we need to find the slant height. Let's call the slant height "l."

Using the Pythagorean theorem, we can set up the following equation:

l^2 = 10^2 + 12^2

Simplifying the equation:

l^2 = 100 + 144

l^2 = 244

Taking the square root of both sides:

l = √244

l ≈ 15.62

Now that we have the perimeter of the base (40) and the slant height (15.62), we can calculate the lateral surface area of the pyramid:

Lateral Surface Area = (40 x 15.62) / 2

Lateral Surface Area ≈ 312.4 square units

Therefore, the lateral surface area of the given pyramid is approximately 312.4 square units.