3.B Three Dimensional Shapes & Space 🌟 Flashcards
How can you find the area of a Circle?
A = πr2
How do you find the area of a Kite?
A = (d1xd2)/2
(angle bisector 1 x angle bisector 2)/2
What is the distance formula?
√(y2 - y1)2 + (x2 - x1)2
How do you get the area of a Triangle?
A = 1/2bh
How do you figure out the area of a Parallelogram?
A = bh
(base x height, length x width)
How do you find the area of a trapezoid?
A = (b1+b2)/2)h
Area = base 1 + base 2 divided by two then multiplied by the height of shape.
How do you find the altitude in a base triangle in an “n” figure?
Use this formula:
a = s/2tan(180/n)
How do you find the total area of a regular polygon?
Use this equation:
Area = n(1/2sa)
Area = number of sides(1/2 x (side length x altitude))
What is a prism?
A prism is a three dimensional solid consisting of two identical polygons on opposite ends called bases.
How do you calculate the total surface area of a prism?
Use this equation:
SA = 2B + Ph
Surface area = 2(area of base) + base perimeter x height of prism
*represents the lateral surface area…
How do you calculate the lateral area of a prism?
LA = Ph
Lateral Area = perimeter of base x height of prism
What is a cylinder?
A cylinder is a three dimensional figure with two circular bases.
How do you calculate the total surface area of a cylinder?
Use this equation:
SA = 2πr2 + 2πrh
SA = 2(base circle area) + (circumference x height of cylinder)
How do you find the lateral area of a cylinder?
LA = 2πrh aka circumference x height of cylinder
How do you find the surface area of a sphere?
4πr2
Basically 4π x radius of sphere squared
How do you figure out the lateral area of a sphere?
You cant. because a sphere has no bases it basically doesn’t have a lateral surface area.
What is true about the relationship between a cylinder and a sphere?
If a cylinder and a sphere have the same radius, the lateral area of the cylinder will be equal to the surface area of the sphere.
What is a pyramid?
A pyramid is a three dimensional solid whose lateral faces are triangles and meet at a point called the apex.
- The base of the pyramid names it.
- The area of all the faces of the pyramid equal the Lateral Area.
What are some of the more common types of pyramids?
- Triangular Pyramids
- Square pyramids
- Rectangular Pyramids
- Regular Pentagonal Pyramids
What is the Apex of a Pyramid?
The Apex of a pyramid is where all lateral faces of a pyramid meet. (Top of the pyramid)
What are the five parts of a pyramid?
- Apex
- Height
- Slant Height
- Apothem
- Base Side
What is the Height of a Pyramid?
The Height of a pyramid is the distance between the base and the apex of the pyramid. (h)
What is the Slant Height of a Pyramid?
The Slant Height of a pyramid is the distance between the midpoint of a side to the apex. (l)
What is the Apothem of a Pyramid?
The Apothem of a Pyramid is the distance from the center of the base to any side of the polygon.
How do you figure out the Surface Area of a Regular Pyramid?
Use this equation:
SA = B + 1/2(P x l)
Surface Area = base area + 1/2(perimeter of base x slant length)
How do you figure out the Lateral Area of a Pyramid?
Use this equation:
LA = n(1/2sl)
Lateral Area = number of sides(1/2(base side length x slant length))
How do find out the Slant Length?
Use the Pythagorean Theorem!
a2 + h2 = l2
- When given a regular triangular pyramid you can use 30 - 60 - 90 Triangle Strategies!
What is a cone?
A three dimensional figure with a circular base with a pointy end.
iT IS MiDnIGHT
IT IS HALLOWEEN
IT iS SpOoKY TIMEEEEEEE
(July 26)
How can you figure out the total surface area of a cone?
SA = B + LA -> SA = πr2 + 2πrl
SA = Area of circular base + (circumference x slant length)
How can you figure out the lateral area of a cone?
LA = 2πrl
What are you?
You are not capable of being perfect because nobody is perfect. You are doing your best and that is what counts. You are loved more than you think, and you are worth the world to me and to a bunch of other people. I care about you, whether you pass this test or not or whether you get over any challenge in you have in your life. You are doing you, and you are doing amazing.
