# Chapter 10

## Chapter 10 Formulas

-Area of a Parallelogram: A=bh

-Area of a Trapezoid: A=1/2(b1+b2)h

-Area of a Circle: A=pi*r^2

-Area of a Triangle: A=1/2*b*h

-Surface Area of a Prism: S=2B+Ph

-Surface Area of a Pyramid: S=B+1/2*P*l

-Surface Area of a Cylinder: S=2(pi*r^2)+(2*pi*r*)h or S=2B+Ch

-Surface Area of a Sphere: S=4*pi*r^2

-Surface Area of a Cone: S=(pi*r^2)+(pi*r*l)

-Volume of a Cylinder: V=pi*r^2*h

-Volume of a Sphere: V=4/3*pi*r^3

-Volume of a Prism: V=Bh

-Volume of a Pyramid: V=1/3*B*h

-Volume of a Cone: V=1/3*B*h

-Perimeter (circumference) of a Circle: C=2*pi*r

-Slant Height: l=square root of (r^2+h^2)

-E+2=F+V (find out if edges, vertices, and faces are correct on a 3-dimensional object)

Notes:

-capital letters in formulas are usually associated with area

## Section 1: Areas of Parallelograms and Trapezoids

Formulas:

Area of a Parallelogram: A=b*h

Area of a Rectangle: A=b*h

Area of a Trapezoid: A=1/2(b1+b2)(h)

-b equals base

-h equals height

-b1 equals first base of trapezoid

-b2 equals second base of trapezoid

Vocabulary:

-base of a parallelogram: The length of any one of a parallelogram's sides.

-height of a parallelogram: The perpendicular distance between the base and the opposite side.

-bases of a trapezoid: A trapezoid's two parallel sides.

-height of a trapezoid: The perpendicular distance between the bases.

Notes:

-parallelogram has same equation for area as rectangle

-the base of a shape is always there but the height doesn't have to be (it can be a hidden

line)

-base is connected to height by a right angle (base is perpendicular to the height)

-trapezoid's bases are always parallel

-with area, units must be squared! ex. in^2

A parallelogram is very similar to a rectangle (^picture is above ^):

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

3. move the triangle to form a rectangle

## Section 2: Areas of Circles

Formulas:

Area of a Circle: A=pi*r^2 (r squared)

-A equals area

-pi= 3.14 or button on calculator

Vocabulary:

-area: The number of square units covered by a figure.

-circle: The set of points in a plane that are the same distance called the radius, from a fixed point, called the center.

-radius: The distance between the center and any point on the circle.

-diameter: The distance across the circle through the center.

-circumference: The distance around a circle.

-pi: The ratio of the circumference of a circle to its diameter.

Notes:

-r^2 (r squared) does not equal the diameter

-if the area is given for a problem, and you want to find the radius (r), divide both sides by pi and then find the square root of both sides to get r by itself

-circle is not a polygon

-with area, units must be squared! ex. in^2

## Section 3: Three-Dimensional Figures

Formulas:

-E+2=F+V (find out if edges, vertices, and faces are correct on a 3-dimensional object)

-E= edges

-F= faces

-V= vertices

Vocabulary:

Solid: A three-dimensional figure that encloses a part of space.

Polyhedron: A solid that is enclosed by polygons.

Prism: A polyhedron, has two congruent .bases that lie in parallel planes. The other faces are rectangles.

Pyramid: Is a polyhedron, has one base, and 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 space that are the same distance from a fixed point called the center.

Edge: The segments where faces of a polyhedron meet.

Vertex: A point where three or more edges meet. (Plural of vertex is vertices.)

Notes:

-solid shape (prism, pyramid) is defined by its base

ex: rectangular prism, rectangular pyramid

-lateral area is the area of the sides (everything but the base/bases)

## Section 4: Surface Areas of Prisms and Cylinders

Formulas:

Surface Area of Prisms/Cylinders: S=2B+Ph

-S=surface area

-B=area of the base

-P=perimeter of the base

-h=height

Vocabulary:

Net: A two-dimensional pattern that forms a solid when it is folded.

Surface Area: The sum of a polyhedron's areas of its faces.

Notes:

-with surface area, units must be squared! ex. in^2

## Section 5: Surface Areas of Pyramids and Cones

Formulas:

Surface Area of a Pyramid: S=B+1/2Pl

Surface Area of a Cone: S=pi*r^2+pi*r*l

-S= surface area

-B= area of the base

-P= perimeter of the base

-l= slant height

-pi= button on calculator/3.14

Vocabulary:

Slant Height: The height of a lateral face, that is, any face not the base.

Notes:

-with surface area, units must be squared! ex. in^2

## Section 6: Volume of Prisms and Cylinders

Formulas:

Volume of a Prism/Cylinder: V=B*h

-V= volume

-B= area of the base

-h= height

Vocabulary:

Volume: A measure of the amount of space a solid occupies.

Notes:

-with volume, unit must be cubed! ex. in^3

## Section 7: Volumes of Pyramids and Cones

Formulas:

Volume of a Pyramid/Cone: V=1/3*B*h

-V= volume

-B= area of the base

-h= height

Vocabulary:

Pyramid: A solid, formed by polygons, that has one base.

Cone: A solid with one circular base.

Volume: The amount of space the solid occupies.

Notes:

-with volume, unit must be cubed! ex. in^3