Question

Стороны основания правильной четырехугольной пирамиды равны 4 см и 8 см а высота равна 12 см. РЕШИТЕ

Answer 1

А какой здесь вопрос?))

Answer 2

Given Information

We are given that the sides of a right quadrilateral pyramid are equal to 4 cm and 8 cm, and the height is 12 cm.

Solution

To solve this problem, we can use the Pythagorean theorem and the formula for the volume of a pyramid.

Step 1: Finding the Base Since the pyramid is right, we can use the Pythagorean theorem to find the length of the base. Let's denote the sides of the base as a and b, where a = 4 cm and b = 8 cm. The height of the pyramid is the perpendicular distance from the apex to the base. Using the Pythagorean theorem, we have:

a^2 + b^2 = h^2

Substituting the given values, we get:

4^2 + 8^2 = h^2

Simplifying, we find:

16 + 64 = h^2

80 = h^2

Taking the square root of both sides, we get:

h = √80

h = 4√5 cm

So, the height of the pyramid is 4√5 cm.

Step 2: Finding the Volume The volume of a pyramid can be calculated using the formula:

Volume = (1/3) * base area * height

The base area of a quadrilateral pyramid can be calculated by dividing it into two triangles and finding the area of each triangle. Since the base is a right quadrilateral, the triangles will be right triangles.

The area of a right triangle can be calculated using the formula:

Area = (1/2) * base * height

Let's calculate the base area of the pyramid:

Base Area = (1/2) * a * b

Substituting the given values, we get:

Base Area = (1/2) * 4 cm * 8 cm

Base Area = 16 cm^2

Now, let's calculate the volume of the pyramid:

Volume = (1/3) * Base Area * height

Substituting the values we found, we get:

Volume = (1/3) * 16 cm^2 * 4√5 cm

Simplifying, we find:

Volume = (16/3) * √5 cm^3

So, the volume of the pyramid is (16/3) * √5 cm^3.

Answer

Therefore, the sides of the base of the pyramid are 4 cm and 8 cm, and the height is 12 cm. The volume of the pyramid is (16/3) * √5 cm^3.