Question

стороны основания правильной четырёхугольной пирамиды равны 8, боковые ребра равны 5. Найдите площадь поверхности этой пирамиды. Пожалуйста, решите с понятным объяснением​

Answer 1

Ответ 112

Решение задания прилагаю

Answer 2

Given Information:

We are given that the sides of the base of a right quadrilateral pyramid are equal to 8, and the lateral edges are equal to 5.

Solution:

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.

Area of the Base:

Since the base of the pyramid is a quadrilateral, we can divide it into two triangles and calculate the area of each triangle separately.

To find the area of a triangle, we can use the formula: Area = (base * height) / 2.

In this case, the base of each triangle is 8, and the height can be calculated using the Pythagorean theorem. The height is the perpendicular distance from the apex of the pyramid to the base.

Let's calculate the height using the Pythagorean theorem: - The hypotenuse is the lateral edge of the pyramid, which is given as 5. - The base of the right triangle is half the length of the base of the quadrilateral, which is 8/2 = 4.

Using the Pythagorean theorem, we can calculate the height: height = sqrt(lateral edge^2 - base^2) = sqrt(5^2 - 4^2) = sqrt(25 - 16) = sqrt(9) = 3.

Now, we can calculate the area of each triangle: Area of each triangle = (base * height) / 2 = (8 * 3) / 2 = 12.

Since there are two triangles, the total area of the base is 2 * 12 = 24.

Area of the Triangular Faces:

The area of each triangular face can be calculated using the formula: Area = (base * height) / 2.

The base of each triangular face is the lateral edge, which is given as 5. The height can be calculated using the Pythagorean theorem.

Using the Pythagorean theorem, we can calculate the height: height = sqrt(lateral edge^2 - base^2) = sqrt(5^2 - 4^2) = sqrt(25 - 16) = sqrt(9) = 3.

Now, we can calculate the area of each triangular face: Area of each triangular face = (base * height) / 2 = (5 * 3) / 2 = 7.5.

Since there are four triangular faces, the total area of the triangular faces is 4 * 7.5 = 30.

Total Surface Area:

The total surface area of the pyramid is the sum of the area of the base and the area of the triangular faces: Total Surface Area = Area of the Base + Area of the Triangular Faces = 24 + 30 = 54.

Therefore, the surface area of the given pyramid is 54 square units.

Please let me know if I can help you with anything else.