You will need

- Paper, pen, calculator

Instruction

1

Polygon lying in the base of the prism may be a right, that is so, all sides equal, and wrong. If the base of the prism lies in a regular polygon, compute its area by the formula S=1/2P*r, where S is the area of a polygon P is the polygon perimeter (sum of lengths of all its sides), and r is the radius of the circle inscribed in the polygon.

2

To visualize the radius inscribed in a regular polygon of a circle is possible, dividing the polygon into equal triangles. The altitude drawn from the vertex of each triangle to the side of the polygon that is the base of the triangle will be the radius of the inscribed circle.

3

If an irregular polygon, to compute the area of a prism you need to split it into separate triangles and find the area of each triangle. Area of triangles is found by the formula S=1/2bh, where S is the area of the triangle b - side, and h is the height drawn to the side b. Once you have calculated the area of all triangles making up the polygon, just sum these areas to get the total area of the base of the prism.

# Advice 2: What is prism

**Prism**- a geometric shape, a polyhedron with two equal and parallel faces, called bases and having the shape of a polygon. The other faces are the bases of their sides are called lateral.

Euclid, Greek mathematician and the founder of elementary geometry, gave this definition of a prism - a solid figure enclosed by two equal and parallel planes (the bases) and lateral faces parallelograms. In ancient mathematics there was no concept of a limited part of the plane, the scientist meant by "bodily shape." Thus, the prism, as well as any other geometrical figure, is not empty.A few basic definitions: • lateral surface – the totality of all the lateral faces. • full surface – the set of all faces (bases and lateral surface); • altitude – line segment perpendicular to the bases of the prism and connecting them; • diagonal – a segment connecting two vertices of the prism that do not belong to the same face; • the diagonal plane is the plane passing through the diagonal of the base prism and its lateral edge; • diagonal cross-section is a parallelogram obtained by the intersection of a prism and a diagonal plane. Special cases of the diagonal of the cross section: rectangle, square, rhombus; • perpendicular to the cross section is a plane passing perpendicular to the side edges.The basic properties of a prism • base of a prism is equal and parallel polygons; • the lateral faces of a prism are always parallelograms; • the lateral edges of the prism are parallel to each other and have equal length.Distinguish between straight and angled right prism: • a right prism, all lateral edges are perpendicular to the base; • oblique prism lateral edges aperpendicular base; • right prism – a polyhedron with a regular polygon at the base and lateral edges are perpendicular to the bases. The right prism is a straight line.Basic numerical characteristics of prisms: • the volume of a prism equals the area of the base in height; • the lateral surface area is the product of the perimeter of the cross section perpendicular to the length of a side edge; • the total surface area of a prism is the sum of all of the areas of the lateral faces and the area of the base multiplied by two.