Chapter 10

Tristin K

Section 1

This sections focuses on the areas of parallelograms and Trapezoids.


The formula to fin the area of a parallelogram is A=b*h

The formula to fin the area of a trapezoid is A=0.5(b1+b2)h

Vocabulary

Base of a parallelogram= Length of any one of its sides.

Height of a parallelogram= The perpendicular distance between the base and the opposite side.

Bases of a trapezoid=Its two parallel sides.

Height of a trapezoid= The perpendicular distance between the basses.

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Example

The formula for it is A=b*h

A=2.5*1.8

A=4.5m2

Do not forget to have squared or else it will be wrong.

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Example of a Trapezoid

The formula A=0.5(b1+b2)*h

A=0.5*(23+15)*9

A=90.5units 2

Now You Try

What is the area of parallelogram 1.


What is the area of Trapezoid 1.


Answer: P=75cm2 T=26m2

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Real Life of a Trapezoid

You might be thinking when would i even need to know the area of a trapezoid. For a trapezoid you might use it to find the area of your lot. some lots can be cut at an angle to suddenly have a trapezoid. Well you want to know how much square feet you have that's when you can use the formula of a trapezoid to fin it out.
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Real Life of a Parallelogram

You would use the area of a parallelogram would be to find how many tiles you want in your bathroom. You would fin the area of each parallelogram and the area of the bathroom and that is how it would show how many you need for the bathroom.

Section 2

This sections focuses on the area of a circle.

The formula for this is A=3.14*r^2.

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 circle.

Pi: The ratio of the circumference of a circle to its diameter.

Example

To find the area you need to follow the formula so. lets say the radius is 2. The formula is A=3.14*r^2. Now you need ti fill in the blank .

A=3.14*2^2

A=12.56units2

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Practice

Now find the area of the circle if its radius is 5m.


Answer=78.5m2

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Real Life

For real life you will need to know the area of a circle a lot. Say you are building a house and you have a window that is a circle well you need to know that right. Well what you can do is follow the formula and get the area to find out how big it needs to be.
Area of a circle

Section 3

This section is based on 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 two congruent bases lying in parallel planes.

Pyramid: A solid. formed by polygons, that has one base. The base can be ant 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: A point at which three or more edges of a polyhedron met.

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Example

Look at the picture above what would it be classified as. Tell if it is a polyhedron or not. If it is tell how many edges,faces, and vertices it has. Do not forget if you forgot any of the vocab go back and review it.


Answer=No, and cylinder

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Practices

Tell me what kind of shape it is and what the faces, edges, and vertices are.



Answer: F=6 E=12 V=8

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Real Life

In real life you might see a three-dimensional object in the world. The coolest is probably is a glass triangular prism. These are used to see rainbow colors just by the sun light.

Section 4

This section focuses on surface areas of prisms and cylinders.

Vocabulary

Net: A two-dimensional pattern that forms a solid when it is folded.

Surface Area: Sum of the areas of its faces.

Example

Lets find the surface area of a prism and cylinder. The formulas are, Prism: S=B+Ph and Cylinder S=2B+Ch or S=2*3.14*r^2+2*3.14*r*h.


Prism:

Cylinder:

Practice

Find the surface area of the prism and the cylinder.


Cylinder=75.36units2

Prism=230m3

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Real Life

Like the picture above the soda cane, can be a cylinder in real life. For the surface area you can find out how much you need if you want a koozie on a cane.
how to make a can cooler | custom wedding Koozies

Section 5

This section is on surface area on cones and pyramids.

The formula for the surface area is S=B+1/2Pl.

Vocabulary

Slant Height: Height of a lateral face, that is, any face that is not the base.
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Example

Lets try out a problem.

Start with the formula S=B+1/2Pl.

Don't forget the BIG B stands for the area of the base, the BIG P is the perimeter of the base' and the l is the lateral surface area.

Then fill it in with the correct number such as,

S=15+1/2*8*4

S=31cm2

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Practice

Now try to find the surface area of a pyramid using the picture above.

Use the formula S=B+1/2Pl.

The base width is 4, base length is 4, and side length is 7


Answer=72units3

Real Life

A real life example could be the Pyramids. The Pyramids are in Egypt. Watch this little video about them below.

Section 6

This section is very easy this one focuses on the volume of prisms and cylinders.

Vocabulary

Volume: A measure of the amount of space it occupies.
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Example

Formula for a prism or cylinder is V=Bh.

You will need to find the area of the base to get the B and then the height is the distance from base to base.

Fill it in,

V=12*6

V=72units3

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Practice

Find the volume of this cylinder, don't forget to us the formula to find the volume of the cylinder, V=Bh.


Answer:1648.5ft3

Real Life

You would use the the formula to find the volume when you are finding how much furniture you can fit in a room. Many people use this to find how big a room is, to other rooms to see what fits the most.
Volume of Prism and Cylinders

Section 7

This section focuses on Volume 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 space the solid occupies.

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Example

Lets do one together.

The formula is V=1/3Bh

So first find the area of the base then the height of the pyramid or cone.
It for the base of a cone would be, 3.14*r^2 or a pyramid would be a l*w.

Know that you know what the BIG B is know find the height.

After you found that fill in the blanch and you will get your volume.

For more help my door is always open in the morning if you need it.

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Practice

Now find the are of this cone for practice.

The length of the radius is 4 and, the height is 5.

Find the Volume.


Answer=87.73units3

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Real Life

The area of a cone or pyramid in real life would be in a cone shaped cup or snow cone. People found out that of you put a cone on a cup it would have almost the same amount of volume. Which cost less paper to make a cup. This helps companies save money and save the planet at the same time.

All the Formulas

A=bh, area of parallelogram

A=1/2(b1+b2)h, area of a trapezoid.

A=3.14r^2, area of a circle.

S=2B+Ph, Surface Area of a prism.

S=2B+Ch, Surface Area of a cylinder.

S=B+1/2Pl, Surface area of a pyramid.

S=3.14r^2+3.14rl, Surface Area of a cone.

V=Bh, Volume of a prism and cylinder.

V=1/3Bh, Volume of a pyramid and cone.

V=4/3*3.14r^3, Volume of a sphere.