Question

Сторона основи правильної трикутної піраміди дорівнює 6 см, а бічне ребро - 5 см. Знайти бічну поверхню піраміди.

Answer 1

Sбок.пов=(1/2)*P*ha
ha - апофема
(ha)²=5²-(6:2)². ha=4
можно без вычислений. прямоугольный треугольник с гипотенузой 5 см(боковое ребро правильной пирамиды) и катетом 3 см (сторону основания пирамиды 6 см:2=3 см) - Пифагоров или Египетский треугольник, => второй катет =4 см (апофема правильной пирамиды)
Sбок.пов=(1/2)*3*6*4
Sбок.пов.=36 см²

Answer 2

Calculation of the lateral surface area of a pyramid

To find the lateral surface area of a pyramid, we need to know the length of the base side and the length of the lateral edge. In this case, the length of the base side is given as 6 cm, and the length of the lateral edge is given as 5 cm.

The formula to calculate the lateral surface area of a pyramid is:

Lateral Surface Area = (Perimeter of the Base) × (Lateral Edge Length) / 2

The perimeter of the base can be calculated by multiplying the length of the base side by the number of sides of the base. Since we are dealing with a triangular pyramid, the base has 3 sides.

Let's calculate the lateral surface area using the given values:

Perimeter of the Base = 3 × (Length of the Base Side) = 3 × 6 cm = 18 cm

Lateral Surface Area = (18 cm) × (5 cm) / 2 = 90 cm² / 2 = 45 cm²

Therefore, the lateral surface area of the given pyramid is 45 cm².