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An inscribed shape is a shape inside of another shape, where it touches all of the sides the shape it is in. To find the area of the outer shape that is not covered, simply find it's area and subtract the area of the inner shape.
For example: A square has a circle inscribed in it. The circle has a radius of 3 inches. What is the area of the square without the circle covering it?
It's area would be 7.73 inches²

A composite shape is 2 shapes that make up one shape. To find the area of one of these, find the area of each shape and add them together.
For example: A shape is consisted of a triangle and a square. The square is 6 units by 6 units and the triangle has a height of 4 units and base of 6 units. What would the area of the whole shape be?
The area would be 48 units²

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(bxh/2)xH (base of the triangular base times the height of the triangular base divided by 2, times the height of the whole figure.) Or if you know the area of the base already, just multiply it by the height.

For example: A triangular prism has a base with a area of 20 units and a height of 15 units.

It's volume would be 300 units cubed.

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V=πr² h/3 (π times the radius squared, times the height divided by three)

For example: A cone shaped container has a radius of 3 inches and height of 6 inches.

It's volume would be 56.55 inches cubed.

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V=a² h/3 (the area of the base times the height divided by three.)

For example: A square pyramid has a height of 6 inches and a base with sides of 4 inches.

It's volume would be 32 inches cubed.

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V=πr² h (pi times the radius squared times the height.)

For example: A cylinder shaped test tube has a height of 4 inches and diameter of one inch.

It's volume is 3.14 inches cubed.

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V=4/3πr3
(4/3 times pi times the radius cubed) is the formula used to calculate the volume of a sphere. For example, if a sphere has a radius of 12 it's volume would be 7238.23.

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What happens when the dimensions of a shape are changed?

The shape will increase or decrease by how much the dimensions are multiplied or divided by.

If one of a square's sides is multiplied by 4 then the area of the square will multiply by 4 as well. If both sides are multiplied by 4, the area of the square will multiply by 8. If the radius of a circle is doubled the circle's area will double as well.

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How to find the surface area of a cylinder

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How to find the surface area of a cylinder

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2πrh+2πr² is the formula for finding the surface area of a cylinder.

In other words, you multiply the radius by pi and the height, and multiply that by 2. Then you find pi times the radius AGAIN square it, and multiply by 2.

For example: A cylinder has a height of 9 and radius of 3. What is it's surface area?

The answer would be 226.19.

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A rectangular prism is made up of  6 rectangles, 4 of the same area and 2 with another area. So you have to add area A * 4 and area B * 2.

For example: The area of one side of a rectangular prism is 24 and the area of another side is 4. What would the surface area be?

The surface area would be 104 because 24 x 4 is 96 and 4 x 2 is 8.

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Like other surface area equations, you simply find the area of each side and add them all together. This shape is composed of 3 rectangles and 2 triangles with the same area. Therefore you find the area of each of the rectangles, and multiply the area of one of the triangles by two. Then you add them together.

For example: A triangular prism has a triangular face with a base of 4 and height of 3. It's rectangular face has a length of 15 and width of 5.

The surface area would be 261 because 36 is the area of the triangles put together and the three rectangles would be 225.

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The formula for the circumference of a circle is C=2πr. C is circumference and r is radius.

For example: A cake has a radius of 3. What is it's circumference?

It's circumference would be 18.85 because 2π3 is 18.85.

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To find the area of a parallelogram you need to multiply its base by its height. The formula for this is A=bh.

For example: A parallelogram has a base of  6 and height of 3. What would it's area be?

It's area would be 18 because 6*3=18.

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A=[(b1+b2)*h]/2

A is area, a is the smaller base, b is the larger base and h is the height.

For example a trapezoid has bases of 5 and 2, and a height of 3. What is it's area?

The area would be 10.5 because 5+2 is 7, which multiplied by 3 is 21. Then divided by 2 is 10.5.

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To find the surface area of a square pyramid you find the area of one of the triangles, and multiply it by four. You also find the area of the base, which is a square.

For example: A square pyramid has a base that is 4 by 4 and each side has a height of 5.

The base would be 16, and each of the sides would be 10. Since there are 4, all the sides together would be 40, which added with 16 is 56.

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The formula for the area of a circle is  π r2

For example: A fruit tart has a radius of 3 inches. What is it's area?

The answer would be 28.27 because pi times 3 squared is 28.27

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To find the area of a rectangle or square, multiply the length and width together. This is also the reason the formula for the triangle works, because one triangle is half of a square.

For example: A rug has a length of 5 feet and a width of 2 feet. What is the area of the rug?

The answer is 10 square feet because 5 * 2 is 10.

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To find the area of a triangle you must use the formula bh/2. This stands for base * height /2.

For example: A triangle has a base of 5 inches and a height of 5 inches. What is the area of the triangle?

The answer would be 12.5 square inches, because 5 * 5 is 25 and 25/2 is 12.5

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Reflections:
The shape is flipped over the x or y axis, one of the numbers switches from negative to positive or vice versa.
Rotations:
The shape is turned a certain number of degrees.
Dialation:
A shape is enlarged, but keeps it's shape.

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Definition: A change in coordinates.
Example: Coordinates (2,1) (5,1) and (2,3) change to (-2,1) (-5,1) and (-2,3)
Non example: The original coordinates in the example above stay the same.
Problem: Flip (3,4) (4,5) and (5,5) over the y-axis.
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Mr. Greene this doesn't sound right to me, but you told us what definition to put and asked us to not ask Google because we would get the wrong answer. I'm really confused about what I'm supposed to do here.

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Definition: A transformation that produces an image that is the same shape as the original, but is a different size.
Example: A shape with sides measuring 5 inches, 10 inches, and 8 inches becomes a shape with sides measuring 4 inches, 9 inches and 7 inches.
Non-example: A shape with the original measurements from the example becomes a shape with sides measuring 6 inches, 10 inches and 8 inches.
Problem: Enlarge a shape with sides measuring 7 inches, 8 inches, and 12 inches by a scale factor of 2.
Answer: 9 inches, 10 inches, and 14 inches.

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Definition: A transformation in which a plane figure turns around a fixed center point.
Example: Coordinates (2,1) (4,1) and (2,4) change to (-2,-1) (-4,-1) and (-2,-4)
Non-example: The original coordinates in my example change to (1,0) (3,0) and (1,3)
Problem: Rotate the coordinates in the example problem 180° counterclockwise.
Answer: (-2,-1) (-4,-1) and (-2,-4)

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Definition: The shape is flipped over the y-axis.
Example: (2,5) (3,5) and (2,6) become (-2,5) (-3,5) and (-2,6)
Non-example: The numbers in the example above become (-2,-5) (-3,-5) and (-2,-6)
Problem: Flip (3,3) (4,4) and (5,4) over the y-axis.
Answer: (-3,3) (-4,4) and (-5,4)

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Definition: A shape is moved a certain direction on the coordinate grid. Every point of the object must be moved in the same direction and for the same distance. The object is not altered in any other way.
Example: (3,2) (5,2) and (5,4) change to (2,2) (4,2) and (4,4)
Non example: (3,2) changes to (2,2) while (5,2) and (5,4) stay the same.
Sample problem: Move (3,3) (4,4) and (3,4) one to the left.
Answer: (2,3) (3,4) and (2,4).

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- Images/pictures are not visible.

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Definition: Each of the pairs of opposite angles made by two intersecting lines.

Picture: Angles A and C are vertical angles because they are made by intersecting lines, and are across from each other. Same goes for D and B.

https://www.mathsisfun.com/geometry/vertical-angles.html ← This is a link to a website discussing vertical angles.

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Definition: The three interior angles of any triangle add up to 180 degrees.

Picture: If angle A is 82° and angle B is 27° we can use the triangle sum theorem to find angle C.

https://www.ck12.org/geometry/triangle-angle-sum-theorem/lesson/Triangle-Sum-Theorem-GEOM/ ← This is a link to a website discussing triangle sum theorem.

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Definition: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Picture and description:

The sides A and B are not more than C when they are put together, therefore the triangle is impossible.

https://www.khanacademy.org/math/geometry/hs-geo-foundations/hs-geo-polygons/v/triangle-inqequality-theorem  This is a video on triangle inequality theorum.

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Definition: Two angles with a sum of 180°.

Picture: Angles A and B add up to 180°.

https://www.khanacademy.org/math/basic-geo/basic-geo-angle/vert-comp-supp-angles/a/complementary-and-supplementary-angles-review ← This is a link to a video on supplementary angles.

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Definition: Adjacent angles have a common side and a common vertex and don’t overlap.

Picture: Angles A and B are adjacent because they have a common side and a common vertex and they don’t overlap.

https://www.mathsisfun.com/geometry/adjacent-angles.html ←This link is to a website discussing ajacent angles.

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Definition: Two angles with a sum of 90°

Picture: Angles A and B add up to 90° https://www.mathsisfun.com/geometry/complementary-angles.html This link is to a website discussing complimentary angles.