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
TRAPEZOIDS
- 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
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
Pi
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