Welcome to Geometry for beginners. This article discusses the three-dimensional pyramid, its area and volume. We are all familiar with the historical significance of the pyramids from the ancient pyramids in Egypt, Mexico, etc. In the modern world, many believe that the pyramid has mystical and / or healing properties. The roofs of many houses and office buildings are actually pyramids, and you will sometimes see fancy boxes for perfumes and / or pyramid-shaped jewelry.
The pyramids are like prisms. The base of both figures can be any polygon, and the figure can be either right or oblique. The difference between the pyramids and prisms is the number of bases. Prisms have two identical parallel bases (above and below), while the pyramids have only one base with all lateral faces meeting at one point. The side faces on the prisms are rectangles or parallelograms. The side faces on the pyramids are always triangles. Since the pyramids are so similar to prisms, you will find that their formulas are similar.
Formula for the surface of the pyramids: SA = B + LA Where SA refers to surface area, B - AREA base, and LA refers to the side area ,
To find the surface area of the pyramid, you begin by calculating the area of the base using the appropriate formula for the polygon forming the base. The second step is to find the lateral area; but this requires a special CAUTION! Remember that each side face is a triangle, and the triangles have the area formula A = 1/2 bh. This is where caution comes about - height, h, repeat the height of the triangle - NOT the height of the pyramid ,
The last step is to simply add all areas together.
The formula for the volume of the pyramids: V = 1/3 Bh where, again, B refers to AREA bases and h reflects the height of the pyramid , Again, ATTENTION! This time h reflects the height of the pyramid - NOT triangular faces , Always check if you use h correctly.
So where did the 1/3 come from? In reality, in geometry classes, we would not get this formula, but instead we would “demonstrate”. Demonstration requires hollow models for prisms and pyramids with the same base and height, as well as WATER! The demonstration is to fill the pyramid model with water and pour this water into a prism. We repeat this process until the prism is filled. Exactly 3 pyramids are required to fill the prism. On the other hand: the volume of the pyramid is 1/3 of the volume of a prism.
Note: Demonstration is NOT proof, but the demonstrated concept is usually remembered longer.
To summarize, the formula for the surface area of the pyramid SA = B + LA and the answer should be marked as square units ; and the formula for the volume of the pyramid is equal to V = 1/3 Bh and the answer should be marked as cubic units ,
