# Chapter 10

## Section 1 - Area of Parallelograms and Trapazoids

Base of A Parallelogram - The length of any side of the parallelogram can be used as the base.

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

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.

How to Find the Area of a Parallelogram

## Section 2 - Areas of Circles

Area - The number of square units covering a figure.

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

Solid - A three-dimensional figure that encloses a space.

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

Net - A two-dimensional representation of a solid. This pattern forms a solid when folded.

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.

Surface Area of a Cylinder | Maths | The Fuse School

## Section 5 - Surface Areas of Pyramids and Cones

Slant Height - The height of any face that is not the base of a regular pyramid.

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

Volume of A Solid - The amount of space the solid occupies.

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)

Calculating the Volume of a Cylinder

## Section 7 - Volumes of Pyramids and Cones

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

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

The volume (V) of a sphere is four thirds the product of Pi and the cube of the radius (r).

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

The volume is also the surface area.