Question

Основаниями для пирамиды служит треугольник со сторонами 6,10,14 см каждое боковое ребро пирамиды наклонено к основанию под углом 45 градусов , выделите объём пирамиды.

Answer 1

R=H 
p=(6+10+14)/2=15 
S=√(15*1*5*9)=15√(3) 
R=6*10*14/4*15√(3)=56/√(3)=H 
V=1/3*S*H=1/3*15√(3)*56/√(3)=56*5=280

Answer 2

Calculating the Volume of the Pyramid

To calculate the volume of a pyramid, we can use the formula:

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

In this case, the base of the pyramid is a triangle with sides measuring 6 cm, 10 cm, and 14 cm. To find the area of the base, we can use Heron's formula, which states that the area of a triangle with sides a, b, and c is given by:

Area = sqrt(s * (s - a) * (s - b) * (s - c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

Let's calculate the volume of the pyramid step by step.

1. Calculate the semi-perimeter of the base triangle: - a = 6 cm - b = 10 cm - c = 14 cm

s = (6 + 10 + 14) / 2 = 30 / 2 = 15 cm

2. Calculate the area of the base triangle using Heron's formula: - s = 15 cm - a = 6 cm - b = 10 cm - c = 14 cm

Area = sqrt(15 * (15 - 6) * (15 - 10) * (15 - 14)) = sqrt(15 * 9 * 5 * 1) = sqrt(675) ≈ 25.98 cm² 3. Calculate the volume of the pyramid using the formula: - Base Area = 25.98 cm² - Height = the height of the pyramid is not provided in the question.

Since the height of the pyramid is not given, we cannot calculate the exact volume without this information. The volume of the pyramid depends on the height, so we need the height value to calculate the volume accurately.

Please provide the height of the pyramid, and I will be able to calculate the volume for you.