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.
