Question

Основание пирамиды правильный треугольник со сторонами 10 см две боковые грани перпендикулярны основанию а третье ребро составляет с основанием 45 градусов найдите площадь боковой поверхности

Answer 1

Sбок.=2SΔ₁+SΔ₂
Нпир.=hосн.⇒Нпир.=√10²-5²=√75=5√3
SΔ₁=1/2*10*5√3=25√3
SΔ₂=1/2*10*√75+75=5√150=25√6
Sбок.=25√3+25√3+25√6=50√3+25√6

Answer 2

Finding the Height of the Pyramid

To find the area of the lateral surface of the pyramid, we first need to find the height of the pyramid. Given that the two lateral faces are perpendicular to the base and the third edge makes a 45-degree angle with the base, we can use trigonometry to find the height.

Let's denote the height of the pyramid as h. Since the third edge makes a 45-degree angle with the base, we can consider the right triangle formed by the height, the third edge, and the base. The base of the triangle is 10 cm, and the angle between the base and the third edge is 45 degrees.

Using trigonometry, we can use the sine function to find the height: sin(45) = h / 10

Simplifying the equation, we have: h = 10 * sin(45)

Now, let's calculate the value of h using this equation.

Calculating the Height

Using the equation h = 10 * sin(45), we can calculate the value of h.

h = 10 * sin(45) h ≈ 10 * 0.7071 h ≈ 7.071 cm

Therefore, the height of the pyramid is approximately 7.071 cm.

Calculating the Area of the Lateral Surface

Now that we have the height of the pyramid, we can calculate the area of the lateral surface. The area of the lateral surface of a pyramid is given by the formula:

Area = (perimeter of the base) * (height) / 2

In this case, the base of the pyramid is an equilateral triangle with sides measuring 10 cm. The perimeter of an equilateral triangle is given by:

Perimeter = 3 * (side length)

Substituting the values into the formula, we have:

Area = (3 * 10) * (7.071) / 2

Simplifying the equation, we get:

Area = 30 * 7.071 / 2

Calculating the value, we have:

Area ≈ 106.065 cm²

Therefore, the area of the lateral surface of the pyramid is approximately 106.065 cm².

Please note that the calculations provided are based on the information given in the question and may not be accurate if the measurements or angles are not precise.