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

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Area of a Trapezoid:

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

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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

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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
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Faces, edges and vertices

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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

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Surface area of a cylinder

S=2TTr2 +2TTrh

S=2TT3*2 +2TT3*7

S=2TT*6 +2TT*21

S=169.56

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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

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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

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Surface area of a sphere

S= 4*TTr*2

S= 4*TT*5*2

S= 125.6

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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

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Volume of a cylinder

V= Bh

V=TTr*2*h

V=TT*7*2*12

V= 527.52

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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

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Volume of a cone

V= 1/3*TTr*2*h

V= 1/3*TT *6*2*12

V= 150.72

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