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?

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.

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.

Volume of a cone