formula for surface area of two dimensional shapes

Because of Plato’s systematic development of a theory of the universe based on the five regular polyhedra, they became known as the Platonic solids. The one remaining regular polyhedra, the dodecahedron, with 12 pentagonal faces, Plato assigned to the heavens with its 12 constellations. In general, the surface area is the sum of all the areas of all the shapes that cover the surface of the object. Plato assigned the tetrahedron, with its sharp points and edges, to the element fire the cube, with its four-square regularity, to earth and the other solids concocted from triangles (the octahedron and the icosahedron) to air and water, respectively. However, the entire group of regular polyhedra owes its popular name to the great Athenian philosopher Plato (428/427–348/347 bc), who in his dialogue Timaeus associated them with the four basic elements-fire, air, water, and earth-that he supposed to form all matter through their combinations. It can be visualized as the amount of paint that would be necessary to cover a surface, and is the two-dimensional counterpart of the one-dimensional length of a curve, and three-dimensional volume of a solid. A tetrahedron is just a triangular pyramid. Area is a quantity that describes the size or extent of a two-dimensional figure or shape in a plane. 300 bc), the octahedron and icosahedron were first discussed by the Athenian mathematician Theaetetus (c. Any prism volume is V BH where B is area of base and H is height of prism, so find area of the base by B 1/2 h (b1+b2), then multiply by the height of the prism. 500 bc) probably knew the tetrahedron, cube, and dodecahedron. Also known as the five regular polyhedra, they consist of the tetrahedron (or pyramid), cube, octahedron, dodecahedron, and icosahedron.

Area is the amount of space occupied by a two-dimensional figure. You can change the units of the area depending on your taste or the overall size of the cone.Platonic solid, any of the five geometric solids whose faces are all identical, regular polygons meeting at the same three-dimensional angles. Area - What is Area Definition, Area of Shapes Formula. (iii) It is a closed figure with three straight sides. The area of the outside surface of a three-dimensional shape or a solid is called Surface Area of that surface. (ii) It has one pair of opposite sides parallel to each other while the other two sides are non-parallel. The surface area of the right cone will then be displayed. Example 3: Match the 2D shape with its property.This is probably the closest answer so far, but still uses information I do not have available in the spreadsheet, which makes it not useful for my purposes. Keep in mind that the height of the cone needs to be greater than zero and that the slant height (if you are entering it) needs to be longer than the radius of the base. 101.5 100 × 2.8 × 5280 43560 67.56 101.5 100 × 2.8 × 5280 43560 67.56. The slant height is the distance between the tip and the outside edge (perimeter) of the base. The next section discusses the main ideas leading up to, and. The height is the perpendicular distance between the cone tip and the center of the circular base. This reasoning connects the geometry of the shape with the algebra of the area or volume formula. Alternatively, you can enter the circumference of the circular base instead.Įnter the height of the cone or the slant height of the cone, depending on which one is known. 2(wl + lh + hw) 'SA'2 (wl+lh+hw) For a rectangular prism with sides w,l,h, the surface area is 'SA'2 (wl+lh+hw) This occurs since there are two pairs of three different faces on every rectangular prism.

You can choose different units of length, depending on the problem or measurement taken. Remember that the radius is half of the diameter of a circle. Let's go through it step-by-step:Įnter a value for the radius of the circular base.

Formula for surface area of two dimensional shapes