# Chapter 10

## 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

## Area of a parellelagram

Words: The area of a parallelogram is the product of the base and the hight

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

## 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)

## Areas of a circle

Words: the area of a circle is the product of pi and the square of the radius

Algebra: A = pi x r (squared)

## Exsample

circle: A = Pi x r squared

A = pi (6) squared = 36 Cm squared

## Classifing solids

Prism- a polyhedron. Prisms have two congregant bases that lie in parallel planes. the other faces are rectangles. a cube is a prism with six faces * 2 bases 5 (plus) faces 0 vertices 9 (plus) *

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

solid- a three dimensional figure that encloses a part of space

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 )

## Surface area of a prism

Words: the surface area of a prism is the sum of twice the area of the base (B) and the product of the base's perimeter (P) and the height (H)

Algebra : S = 2B + Ph

## Surface area of a cylinder

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

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

## Vocab

net- a net is a two dimensional pattern that forms a solid when its folded

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

## surface area of a pyrimid

Words: the surface area of a regular pyramid (rectangular) is the sum of the area of the base (B) and one half the product of the base perimeter (P) is and the slant height (L) ( a squared + b squared = c squared )

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

## surface area of a cone

Words: the surface area of a cone is the sum of the area of the circular base with radius (r) and the product of pi, the radius (r) of the base, and the slant height (L) (a squared + b squared = c squared)

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

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## 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

## 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