# Chapter 10

### Erich B

## Section 1 - Area of Parallelograms and Trapazoids

Height of A Parallelogram - The perpendicular distance between the side whose length is the base and the opposite side.

1. Start with any parallelogram.

2. Cut the parallelogram to form a right triangle and a trapezoid.

3. Move the triangle to form a rectangle.

The area of a parallelogram: A=(b1+b2)h

Bases of A Trapezoid - The lengths of the parallel sides of the trapezoid.

Height of A Trapezoid - The perpendicular distance between the bases of the trapezoid.

The area of a trapezoid: A=1/2(b1+b2)h

Real life example: You are in math class, and you are working on finding the area of trapezoids and parallelograms. You need to calculate the area of a parallelogram and a trapezoid.

## Section 2 - Areas of Circles

The area (A) of a circle is the product of Pi and the square of the radius (r).

A=(Pi*r^2)

Real life example: you got a flat tire on your car, and you need to get a new one but you don't know how big the tire should be. You have to calculate the area of your other tires to find the right size.

## Section 3 - Three-Dimensional Figures

Polyhedron - A solid that is enclosed by polygons.

Face of A Polyhedron - A polygon that is a side of a polyhedron.

Prism - A solid, formed by polygons, that has two congruent bases lying in parallel planes.

Pyramid - A solid, formed by polygons, that has one base. The base can be any polygon, and the other faces are triangles.

Cylinder - A solid with two congruent circular bases that lie in parallel planes.

Cone - A solid with one circular base.

Sphere - A solid formed by all points in a space that are the same distance from a fixed point called the center.

Edge of A Polyhedron - A line segment where two faces of the polyhedron meet.

Vertex of A Polyhedron - A point at which three or more edges of a polyhedron meet.

Real life example: You are an artist, and you need to draw a new shape, but it has to be three-dimensional. You need to draw a three-dimensional shape.

## Section 4 - Surface Areas of Prisms and Cylinders

Surface Area of A Polyhedron - The sum of the areas of the faces of the polyhedron.

The surface area (S) of a prism is the sum of twice the area of a base (B) and the product of the base's perimeter (P) and the height (h).

S=(2*B+P*h)

The surface area (S) of a cylinder is the sum of twice the area of a base (B) and the product of the base's circumference (C) and the height (h).

S=(2*B+C*h)=(2*Pi *r^2)+(2*Pi*r*h)

Real life example: You work at a recycling plant, and you need to measure cans to find out if they will fit in the crusher. You need to calculate the surface area of the cans.

## Section 5 - Surface Areas of Pyramids and Cones

The surface area (S) of a regular pyramid is the sum of the area of the base (B) and one half of the base perimeter (P) and the slant height (l).

S=(B+1/2*P*l)

The surface area (S) of a cone is the sum of the area of the circular base with radius (r) and the product of Pi, the radius of the base, and the slant height (l).

S=(Pi*r^2+Pi*r*l)

## Section 6 - Volume of Prisms and Cylinders

The volume (V) of a prism is the product of the area of the base (B) and the height (h).

V=(B*h)

The volume (V) of a cylinder is the product of the area of the base (B) and the height (h).

V=(B*h)=(Pi*r^2*h)

## Section 7 - Volumes of Pyramids and Cones

V=(1/3*B*h)

The volume (V) of a cone is one third the product of the area of the base (B) and the height (h).

V=(1/3*B*h)=(1/3*Pi*r^2*h)

Real life example: You are an architect and you need to design a pyramid for tourism, but tourists need to be able to go inside. You need to calculate the volume of the pyramid in order to have it hollowed out.

## Extra Information

V=(4/3*Pi*r^3)

The volume is also the surface area.