Question

В основании пирамиды равнобедренный треугольник, у которого одна сторона = 40 см, а две другие = 25 см. Высота пирамиды проходит через вершину угла образованного равными сторонами основания и = 8 см. Определить боковую поверхность пирамиды

Answer 1

Обозначим треугольник в основании через АВС,
со сторонами АВ=ВС=25см и стороной АС=40см
и высотой КВ=8см
По теореме Пифагора
в треуг.АВК
АК^2=АВ^2+ВК^2=8^2+25^2=64+625=689см
АК=_/689==26.2см
треуг.АВК=треуг.КВС =>
АК=КС==26.2см
Рпир.=Р тр.АВК+Р тр.КВС+Р тр.АКС
Р пир=(25+8+26.2) ×2+26.2+26.2+40=
=59.2×2+92.4=118.4+92.4=220.8см

Answer 2

Calculation of the lateral surface area of the pyramid

To calculate the lateral surface area of a pyramid, we need to know the slant height of the pyramid. The slant height can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, we have a right triangle formed by the height of the pyramid, the slant height, and half of the base of the pyramid. Let's denote the height of the pyramid as h, the slant height as l, and half of the base as b/2.

Using the Pythagorean theorem, we can write the equation:

l^2 = h^2 + (b/2)^2

Given the information provided, we know that one side of the base is 40 cm and the other two sides are 25 cm. This means that the base of the pyramid is an isosceles triangle, and the height of the pyramid passes through the vertex of the angle formed by the equal sides of the base.

We also know that the height of the pyramid is 8 cm.

Let's substitute these values into the equation and solve for the slant height:

l^2 = 8^2 + (40/2)^2

l^2 = 64 + 400

l^2 = 464

Taking the square root of both sides, we find:

l ≈ 21.54 cm

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

Lateral Surface Area = (Perimeter of the base) * (Slant height / 2)

The perimeter of the base can be calculated by adding up the lengths of all three sides of the base.

In this case, the base is an isosceles triangle with two sides measuring 25 cm and one side measuring 40 cm. Therefore, the perimeter of the base is:

Perimeter = 25 + 25 + 40 = 90 cm

Substituting the values into the formula, we get:

Lateral Surface Area = 90 * (21.54 / 2) = 967.65 cm^2

Therefore, the lateral surface area of the pyramid is approximately 967.65 cm^2.

Please note that the calculations are based on the information provided and the assumption that the pyramid is a regular pyramid with an isosceles triangle as the base.