Question

ПОМОГИТЕ СРОЧНО!!!ПОМОГИТЕ!!Апофема правильної піраміди дорівнює l і утворює кут альфа з бічним ребром. Знайдіть площу повної поверхні піраміди,якщо піраміда чотирикутна

Answer 1

дивись малюнок уважно!!! OK gthgtyl/CD, DK=KC ,SK перпенд.DC по т. про три перпендикуляра,SK апофема

tq a=DK/l, DK=l*tg a, DC=2l*tg a

S основ.=4*l^2*tg^2a( в основі квадрат)

S грани(DSC)=SK*DK

S бп=4*SK*DK=4*l*ltg a=4*l^2*tg a

S=4*l^2*tg^2a+4*l^2*tg a=4*l^2*tg a*(1+tg a)

Answer 2

Apothem of a Pyramid and Surface Area Calculation

The apothem of a pyramid is a line segment drawn from the center of the base to the midpoint of any of the triangular faces. To find the surface area of a pyramid, we need to know the length of the apothem, denoted as 'l', and the angle formed between the apothem and one of the lateral edges, denoted as 'alpha' (α).

In the given problem, we are told that the apothem of the pyramid is 'l' and it forms an angle 'alpha' (α) with one of the lateral edges.

To find the surface area of the pyramid, we need to calculate the area of the base and the area of the four triangular faces.

Calculation Steps

1. Calculate the area of the base: - Since the pyramid is described as a four-sided pyramid, we can assume it has a square base. - The area of a square is calculated by squaring the length of one of its sides. - Let's denote the length of one side of the square base as 's'. - Therefore, the area of the base is s^2.

2. Calculate the area of the four triangular faces: - Each triangular face of the pyramid is an isosceles triangle with the base equal to 's' and the height equal to 'l'. - The area of an isosceles triangle can be calculated using the formula: (base * height) / 2. - Therefore, the area of each triangular face is (s * l) / 2. - Since there are four triangular faces, the total area of the four faces is 4 * (s * l) / 2.

3. Calculate the total surface area of the pyramid: - The total surface area of the pyramid is the sum of the area of the base and the area of the four triangular faces. - Therefore, the total surface area is s^2 + 4 * (s * l) / 2.

Conclusion

To find the surface area of the given pyramid, you need to know the length of one side of the square base ('s') and the length of the apothem ('l'). Then, you can use the formula s^2 + 4 * (s * l) / 2 to calculate the total surface area of the pyramid.

Please let me know if you need any further assistance!