Question

Объем правильной четырехугольной пирамиды 80дм^2, а высота 5 дм. Найти площадь боковой поверхности

Answer 1

Значит основание -квадрат 
V= Sосн х H и тогда S= 16дм^2. И сторона корень из 16 = 4дм
Sбок=1\2Р х L(апофема) 
Находим апофему по т. Пифагора 5^2+2^2=L
L= корень из 29 
Sполн.= 8х корень из 29 дм^2

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 base area and the slant height of the pyramid. In this case, we are given that the base area of the pyramid is 80 dm^2 and the height is 5 dm.

Let's calculate the slant height of the pyramid first. We can use the Pythagorean theorem to find it. The slant height (l) can be calculated using the formula:

l = sqrt(h^2 + (a/2)^2)

where h is the height of the pyramid and a is the length of one side of the base.

In this case, h = 5 dm and the base is a square, so all sides are equal. Let's assume the length of one side of the base is s.

l = sqrt(5^2 + (s/2)^2)

Now, let's calculate the value of s. Since the base area is given as 80 dm^2, we can find the length of one side of the base (s) using the formula:

s = sqrt(A)

where A is the area of the base.

s = sqrt(80) = 8.944 dm

Now, we can substitute the values of h and s into the formula for l:

l = sqrt(5^2 + (8.944/2)^2) = sqrt(25 + 39.999536) = sqrt(64.999536) = 8.062 dm

Now that we have the slant height (l), we can calculate the lateral surface area (S) of the pyramid using the formula:

S = (1/2) * p * l * a

where p is the perimeter of the base and a is the apothem (the distance from the center of the base to the midpoint of one of the sides).

Since the base is a square, the perimeter (p) is given by:

p = 4 * s = 4 * 8.944 = 35.776 dm

The apothem (a) can be calculated using the formula:

a = s/2 = 8.944/2 = 4.472 dm

Now, let's substitute the values of p, l, and a into the formula for S:

S = (1/2) * 35.776 * 8.062 * 4.472 = 722.5 dm^2

Therefore, the lateral surface area of the pyramid is 722.5 dm^2.