You will need

- properties of the pyramid;
- - trigonometric functions;
- the similarity of figures;
- - finding the areas of polygons.

Instruction

1

The area of the larger base

**of the pyramid**is*the area*of the polygon that represents it. If this is the right pyramid, its base lies a regular polygon. To know his*area*enough to know the only one of its sides.2

If the large base is a right triangle, find its

*area*by multiplying the square of side square root of 3 divided by 4. If the base is a square, erect his side in the second degree. In General, for any regular polygon, use the formula S=(n/4)•a2•ctg(180º/n), where n is the number of sides of a regular polygon, a is the length of its side.3

The side of the smaller base of the find, according to the formula b=2•(a/(2•tg(180º/n))-h/tg(α))•tg(180 ° /n). Here the a – side of the larger base, h – height of the truncated

**pyramid**, α is the dihedral angle at its base, n is the number of sides**of the bases**(it is the same). The area of the second base look similar to the first, using the formula the length of its sides S=(n/4)• b2•ctg(180º/n).4

If the reasons are other types of polygons, all known one

**reason**, and one of the sides of the other, the other hand, calculate as such. For example, the side of larger base 4, 6, 8 see the Big side of the smaller base of the wound is 4 cm. Calculate the coefficient of proportionality, 4/8=2 (take the large side in each of the**bases**), and calculate the other sides 6/2=3 cm, 4/2=2, see Receive side 2, 3, 4 cm smaller base side. Then, calculate their area, as the areas of triangles.5

If you know the ratio of the corresponding elements of the truncated pyramid, the ratio of the areas

**of the bases**is equal to the ratio of the squares of these elements. For example, if you know the corresponding sides**of the bases**a and A1, A2/A12=S/S1.