Chapter 10
Isa W.
10.1- Area of Parallelograms and Trapezoids
Vocabulary:
- Base of a parallelogram- the length of any one of its sides
- Height of a parallelogram- the perpendicular distance between the base and the opposite side
- Base of a trapezoid- its two parallel sides
- Height of a trapezoid- the perpendicular distance between the bases
Formula for a parallelogram:
A=bh
Area of a Trapezoid:
A=1/2*(b1+b2)*h
10.2- Area of a Circle
Vocabulary:
- Area- the number of square units covered by a figure
- Circle- the set of all 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 the a circle
- Pi- the ratio of the circumference of a circle to its diameter
Formula for the area of a circle:
A=TT*r2
10.3- Three- Dimensional Figures
Vocabulary:
- Solid- A three- dimensional figure that encloses a part of space
- Polyhedron- A solid that is enclosed by polygons
- Face- A polygon that is a side of a polyhedron
- Prism- A solid, formed by polygons, that has two congruent bases lying in parallel lines
- 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 space that are the same distance from a fixed point called the center
- Edge- A line segment where two faces of the polyhedron meet
- Vertex- The endpoint at which three or more edges of a polyhedron meet
How to classify a solid
To classify a solid, you look at the shape of the base
Faces, edges and vertices
10.4- Surface Areas of Prisms and Cylinders
Vocabulary:
- Net- a two- dimensional representation of a solid. This pattern forms a solid when it is folded
- Surface Area- the sum of the areas of the faces of a polyhedron
How to find the surface area of a triangular prism
S=2B+Ph
S=(1/2*2*6)+(7+7+2)*9
S=198
Surface area of a cylinder
S=2TTr2 +2TTrh
S=2TT3*2 +2TT3*7
S=2TT*6 +2TT*21
S=169.56
A tent is a triangular prism. To figure out how much space the tent would take up, you would use the formula for the surface area of triangular prism.
10.5- Surface Areas of Pyramids and Cones
Vocabulary:
- Slant height- the height of the lateral facs
Surface area of a pyramid
S=B+1/2*P*l
S=50.41+1/2*14.2*6.6
S=4,771.28
Surface area of a cone
S=TTr*2 +TTr*l
S=TT*5.7*2 +TT*5.7*12
S= 35.79 + 26.37
S= 62.16
Surface area of a sphere
S= 4*TTr*2
S= 4*TT*5*2
S= 125.6
10.6- Volumes of Prisms and Cylinders
Vocabulary:
- Volume- a measure of the amount of space it occupies
Volume of a prism
V=Bh
V=l*w*h
V= 4*5*10
V= 200
Volume of a cylinder
V= Bh
V=TTr*2*h
V=TT*7*2*12
V= 527.52
A can of soup is a cylinder. To figure out how much soup is in the can, you would need to use the formula for the volume of a cylinder.
10.7- Volumes of Pyramids and Cones
Vocabulary:
- Pyramid- a solid, formed by polygons, that has one base. The base can be any polygon, and the other faces are triangles
- Cone- a solid with one circular base
- Volume- the amount of space the solid occupies
Volume of a pyramid
V=1/3Bh
V= 1/3*48*8
V= 128
Volume of a cone
V= 1/3*TTr*2*h
V= 1/3*TT *6*2*12
V= 150.72
The pyramids in Egypt are rectangular pyramids. The find the volume of them, you would use the formula V=1/3Bh.
To find how much ice cream could fit in an ice cream cone, you would use the formula V= 1/3*TTr*2*h
Variables
A= area
b=base
h=height
B= area of base
P=perimeter of base
C= Circumference
r= radius
l= slant height
d= diameter
SA= surface area
TT= pi
s= side length