Chapter 10

10.1: Areas of Parallelograms and Trapezoids

Vocab

  • Base of a parallelogram: The length of any side of the parallelogram can be used as the base.
  • Height of a parallelogram: The perpendicular distance between the side whose length is the base and the opposite side.
  • Base of a trapezoid: The lengths of the parallel sides of the trapezoid.
  • Height of a trapezoid: The perpendicular distance between the bases of the trapezoid.
Formulas


  • Parallelogram: A=b*h Write formula for area.
A=8*10 Substitute the base and height for b and h.


A= 80 Multiply.


  • Trapezoid: A=0.5(b1 + b2)h Write formula for a trapezoid.
A=0.5(31 + 77)25 Substitute b1, b2, and h for the bases and the height.


A=0.5(108)25 Add b1 and b2 together.

A=54*25 Multiply 0.5*b.

A=1350 Multiply.

Practice Problems


  • Find the area of a trapezoid with a height of 5 inches, a base 1 of 9 inches, and a base 2 of 18 inches.
(405 inches squared)


  • Find the area of a parallelogram that has a base of 10 feet and a height 21.5 feet.
(215 ft squared)

Real Life Situations


  • You need to design a garden in your lawn in a corner that you want the shape as a parallelogram. Along the wall you have 4 feet and 6 feet. You will need 24 feet of boarding. SInce you already have 2 of the 4 walls done, you just get 12 feet of wood boards to perfectly fit the garden in.
HOW TO FIND THE AREA OF A TRAPEZOID: THE EASY WAY!

10.2: Areas of Circles

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.
  • Circumference: The distance around a circle.
  • Diameter: The distance across the circle through the center.
  • Pi: The ratio of the circumference of a circle to its diameter.
Formulas:
  • Area of a circle: A=pi*r^2
A=pi*r^2 Write formula for area.

A=3.14(5)^2 Substitute 3.14 for pi and 5 for r

A=78.5 Evaluate using a calculator


  • Finding the radius of a circle:
A=pi*r^2 Write formula for area of a circle.

530.66=(3.14)r^2 Substitute 530.66 for A and 3.14 for pi.

169 = r^2 Divide each side by 3.14

√169 = r Take positive square root of each side.

13 = r Evaluate square root.

Practice Problems:

  • Find the area of a circle with the diameter of 16 inches.
(200.96 inches squared)


  • FInd the area of a circle with a radius of 8 inches.
(200.96 inches squared)


Real Life Situations:

Your boss at work needs you to design a new kind of rug. He asks you to make it with the radius of 8 feet.

Area of a Circle

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 the polyhedron.
  • Prism: A solid, formed by polygons, that has 2 congruent bases lying in parallel planes.
  • Pyramid: A solid, formed by polygons, that has 1 base. This base can be any polygon, and the other faces are triangles.
  • Cylinder: A solid with two congruent circular bases that lie in parallel plains.
  • Cone: A solid with 1 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 2 faces of the polyhedron meet.
  • Vertex: A point at which three or more edges of a polyhedron meet.
Formulas:


  • None D:
Practice Problems:



  • How many edges does a pentagonal pyramid have? (10)
  • Sketch a triangular prism.
Real Life Situations:



  • Your kids are getting into egyptian gods and pharaohs. He wants a pyramid toy. Instead of you buying one you decide to make one yourself. You need the amount of vertices and edges and faces. You make the pyramid.
Classify Three-Dimensional Figures

10.4: Surface Area 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 the polyhedron.

Formulas:
  • Surface Area of a prism: S=2B+Ph
B=area of the base

P=perimeter of the base

S=2B+Ph

S=2(20*5)+(13+13+10+10)7

S=522


  • Surface area of a cylinder: S=2B+Ch = 2(pi)r²+2(pi)rh
S=2(pi)r²+2(pi)rh

S=2(pi)4²+2(pi)4*10.7

S=pi*8+pi*85.6

S=25.12+268.784

S=369.45


Practice Problems:

  • Find the surface area of a cylinder that has a radius of 6inches, a height of a 10 inches.
(602.88inches³)


  • Find the surface area of a prism with a rectangular base which has length of 10 inches, a height of 95 inches, and a hypotenuse of 95.5 inches, while the prism has a height of 65 inches.
(3504 inches²)


Real Life Situations:

  • Your boss at work needs you to paint the meeting room with a new design. You need to find out how much paint you need exactly to be able to tell him how much money you need.

Cylinder Volume and Surface Area

10.5: Surface Areas of Pyramids and Cones

Vocabulary:

  • Slant Height: The height of any face that is not the base of a regular pyramid.
Formulas:

  • Surface area of a pyramid: S= B+0.5Pl
S=27.7 + 0.5(24)(6)

S=99.7

  • Surface area of a cone: S=(pi)r^2+(pi)rl
S=(pi)4^2+(pi)(4)(9)

S=(pi)16+(pi)36

S=183.4

  • Getting the slant height of a Pyramid: A^2+B^2=C^2.
  • Getting the slant height of a Cone: r^2+h^2=C^2
Practice Problems: (See the picture before the video)


Real life situations:

Your boss at work needs you to create a new type of ice cream cone that kids will like. It needs to be wider than 2 inches and it is as tall as 8 inches. What is the slant height of the ice cream cone?

Big image
Mrs. Parker's Math Class - Surface Area of Pyramids and Cones

10.6: Volumes of Prisms and Cylinders

Vocabulary:


  • volume: The amount of space the solid occupies.
Formulas!:



  • Volume of a prism: V=Bh (B is also l*w or the way to get the area of the solid's base)
  • Volume of a Cylinder: V=Bh (B is (pi)r^2)
Practice Problems:



  • Look below again.
Real Life Situations:

  • Your boss wants to make a new tissue box that can only hold a certain amount of tissues. You need to find the volume of the tissue box to find out how many can fit.

Big image
Solid Geometry Volume

10.7: Volumes of Pyramids and Cones

Vocabulary:
  • Pyramid: A solid, formed by polygons, that has 1 base. This base can be any polygon, and the other faces are triangles.
  • Cone: A solid with 1 circular base.
Formulas:


  • Volume of a Pyramid: V=(1 third)Bh
  • Volume of a Cone: V=(1 third)(pi)r^2h
Practice Problems:


You know the drill already, me.

Real Life Situation:

Your boss needs you to find out how much ice cream an ice cream cone can hold. The radius is 1.5 inches and the height is 10 inches.

Big image
Volume of a cone