Advice 1: How to find the lateral surface area of a pyramid

Under the pyramid is understood one of the varieties of polyhedra, which is formed from the base of the polygon and triangles, which are its faces, and unite in one point - the top of the pyramid. Find the area of the lateral surface of the pyramid will not make special difficulties.
How to find the lateral surface area of a pyramid
Instruction
1
First of all, it should be understood that the lateral surface of the pyramid is represented by several triangles, the square of which can be found through a variety of formulas, depending on known data:

S = (a*h)/2, where h is the height lowered on the side of a;

S = a*b*sinβ, where a, b are the sides of a triangle, and β is the angle between these sides;

S = (r*(a + b + c))/2, where a, b, c be the sidelengths of triangle and r is the radius of the inscribed in the triangle circumference;

S = (a*b*c)/4*R, where R is the radius of the circle circumscribed around the triangle;

S = (a*b)/2 = r2 + 2*r*R (if the triangle is rectangular);

S = S = (a2*√3)/4 (if the triangle is equilateral).

In fact, it is only the most basic of well-known formulas for finding the area of a triangle.
2
Calculating using the above formulas the area of all the triangle faces of the pyramid, you can begin calculating the square of the side surface of the pyramid. This is done very simply: you add together the area of all triangles forming the lateral surface of the pyramid. The formula can be expressed as:

SN = ΣSi, where SN is the lateral surface area of a pyramid, Si - the area of the ith triangle as part of its side surface.
3
For clarity, we can consider a small example: given a right pyramid, the side faces of which is formed by the equilateral triangles and base is square. The edge length of the pyramid is 17 cm you want to find the lateral surface area of the pyramid.

Solution: a known edge length of the pyramid, we know that her face is an equilateral triangle. Thus, we can say that all sides of all triangles of the side surface is equal to 17 cm is Therefore in order to calculate the area of any of these triangles, you will need to use the formula:

S = (172*√3)/4 = (289*1.732)/4 = 125.137 cm2

It is known that at the base of the pyramid is a square. Thus, it is clear that these equilateral triangles four. Then the lateral surface area of a pyramid is calculated as follows:

125.137 cm2 * 4 = 500.548 cm2

Answer: the lateral surface area of a pyramid is 500.548 cm2

Advice 2: How to calculate the area of a pyramid

Under area of a pyramid is usually defined as the area of its side or full surface. The basis of this geometry is the polygon. The side faces have a triangular shape. They have a common vertex, that is simultaneously the pinnacle of the pyramid.
How to calculate the area of a pyramid
You will need
  • - a sheet of paper;
  • - handle;
  • calculator;
  • the pyramid with the specified parameters.
Instruction
1
Consider this in the task pyramid. Determine correct or incorrect polygon lying at its base. On the right, all sides are equal. The area in this case is equal to half the product of the perimeter to the radius of the inscribed circle. Find the perimeter by multiplying the side length l on the number of parties n, that is, P=l*n. To Express the area of the Foundation can be a formula of Ln=1/2P*r, where P is perimeter and r is the radius of the inscribed circle.
2
Perimeter and area of an irregular polygon are calculated differently. The sides are of different length. To calculate the perimeter is to add all the segments, limiting the basis. To compute the area run an additional build. Divide the irregular polygon in shape, the parameters of which you are aware of, and the area you can easily find using the most common formulas and trigonometric functions.
3
The lateral surface of a pyramid is the sum of all the lateral faces. The right pyramid of height falls in the center of the base regular polygon. For clarity, it is very helpful to build most of the height of the pyramid and one of its sides. The intersection of the second height to the bottom face connect with the center of the base. In any case, get a rectangular triangle, in which you need to calculate the hypotenuse, and the height of the side faces. Do so using your known parameters (for example, the height of the pyramid and the radius of the inscribed in the polygon of the base circle).
Build the height of the side faces
4
Knowing the height of the right side face of the pyramid, compute the lateral surface area. It is equal to half the product of the perimeter of the base to the height of the side faces, that is to calculate it by the formula SB=1/2P*h, where P is the already known perimeter, and h is the height of the side faces.
5
The calculation of the lateral surface of the irregular pyramid will require several time-consuming. It is equal to the sum of the areas of all lateral faces. Remember, what is the area of a triangle. It can be found by the formula S=1/2l*h, that is, polypropilenium the base of the triangle to its height.
6
Find the surface area of the pyramid. To do this, fold the already known base area and lateral surface.
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