# Chapter 10

### Veronica S.

## Formulas

**Parallelogram**: A = b x h

**Trapezoid**: A = 1/2 (b1 + b2) x h

**Circle**: A = Pi x r squared C = Pi x D or 2 x Pi x r

**Prism**: Surface A = 2 x B + P x h (B = area of base, P = perimeter of base) V = b x h

**Cylinder**: S = 2 x B + C x h (B = area of base, C = circumference)

(Can also be written as: 2 x Pi x r squared + 2 x Pi x r x h)

V = b x h (Can also be written as: Pi x r squared x h)

**Pyramid:** S = B + 1/2 x P x L (L = slant height), V = 1/3 x B x H

**Cone**: S = Pi x r squared + Pi x r x L V = 1/3 x B x H (Can also be written as 1/3 x Pi x r squared x H)

**Triangle**: A = 1/2 x b x h

**Sphere**: A = 4 x Pi x r squared V = 4/3 x Pi x r cubed

**cube**: S= 6 x a squared V= s cubed ( s = side )

**hexagonal prism**: S= 6 x s x h + 3 x (square root of 3) x s squared V= 3 x 3 ( <-square root) divided by 2 x s squared x h

## Section 1 -Areas of Parallelograms and Trapezoids

## Area of a parellelagram

Algebra: A=bh

## Area of a Trapezoid

Words: the area of a trapezoid is one half times the product of the sum of the bases and the height.

Algebra: A = 1/2 x (b1 + b2) x h

## RHOMBUS - when finding the height for finding the area you must find the first vertical point from base to base as shown in the picture | ## TRAPEZOIDS - when finding the area of a trapezoid you need to find the bases, base 1 and base 2 - after you find b1 and b2 you multiply 1/2 * h * (b1 + b2) | ## PARELLELOGRAMS- the area of a square is the product of the base and height, so the formula for the area of a parallelogram is always A = bh |

## RHOMBUS

## TRAPEZOIDS

- after you find b1 and b2 you multiply 1/2 * h * (b1 + b2)

## Examples

Parallelogram: A = b x h

A = 5 x 3 = 15 Cm (squared)

Trapezoid: A = 1/2 (b1 + b2) x h

A = 1/2 (4 + 8) x 3 = 18 m (squared)

## Real life exsamples

## Section 2- Areas of circles

## Areas of a circle

Algebra: A = pi x r (squared)

## Exsample

A = pi (6) squared = 36 Cm squared

## Radius Radius is half the diameter, if it asks for you to use radius (r) but the picture/ formula gives diameter simply divide it by 2, same with the opposite- it gives radius then just multiply by 2 | ## Pi Remember to use either the pi button or 3.14 depending on if the teacher says or if it says round to the nearest tenth then use pi button if it says exact answer then use 3.14 |

## Radius

## Section 3- three dimensional figures

## Classifing solids

Pyramid- a polyhedron. pyramids are classified by their basses, they have one base and all other sides are triangles * 1 bases 4 (plus) faces 1 vertices 12 (plus) edges *

Cylinder- a solid with two congruent circular bases that lie in parallel planes * 2 bases 0 faces 0 vertices 0 edges *

Cone- a solid with one circular base * 1 base 0 faces 0 vertices 0 edges *

Sphere- a solid formed by all points in space that are the same distance from a fixed point called the center * 0 bases 0 faces 0 vertices 0 edges *

## Vocab for section 10.3

polyhedron- a solid that is enclosed by polygons, has only flat surfaces.

faces- polyhedron that enclose a solid

edge- segments where faces of a polyhedron meet

vertex- a point where three or more edges meet ( plural = vertices )

## Examples in real life

## Section 4 -surface areas of prisms and cylindars

## Surface area of a prism

Algebra : S = 2B + Ph

## Surface area of a cylinder

Algebra: S = 2B + Ch = 2 x pi x r squared + 2 x pi x r x h

## examples in real life

## Vocab

surface area- used for polyhedron. the surface area is the sum of the area of its faces.

## nets

## section 5- areas of pyramids and cones

## surface area of a pyrimid

Algebra: S = B + 1/2 x P x L

## surface area of a cone

Algebra: S = pi x r x l

## Things to remember

pyramid: for a regular pyramid the slant height is the same on every face except the base. the height of any pyramid is the perpendicular distance between the vertex and the base. the slant height for a regular pyramid is the height of a lateral face that isn't the base.

cone: you can use the net of a cone to find its surface area. the curved surface of a cone is a section of a circle with the radius (L), the slant height of the cone.

TO FIND SLANT HEIGHT YOU DO a squared + b squared = c squared ( such as the height squared + the radius squared = the slant height

## section 6 -Volumes of prisms and cylders

## Volume of a prism

Words: the volume of a prism is the product of the base (B) and the height (h)

Algebra: V = B x h

## Volume of a cylinder

Words: the volume of a cylinder is the product of the area of a base (B) and the height (h)

Algebra: V = B x h

...................= pi x r squared x h

## Things to remember

cylinder: The base of a cylinder is a circle so its area is A = pi x r squared

prism: when you find the volume of a triangular prism be carful not to confuse the height of the prism with the height of the triangular base

## section 7- Volumes of pyramids and cones

## how to find the volume of a pyramid

words: the volume of a pyramid is one third the product of the base (B) and the height (h)

algebra: V = 1/3 x B x h

## how to find the volume of a cone

words: the volume of a cone is one third the product of the base (B) and the height

algebra: V = 1/3 x B x h

...................= 1/3 x pi x r squared x h