Characteristics of Prisms
Cubes have these many faces, which are the flat surfaces of the solid.
What are 6?
The area of this 2D shape is found by multiplying its sides, as they are all the same.
What is a square?
The surface area of a cube with side lengths of 2 cm is equal to this.
What is 24 cm2?
How:
SA of a cube = 6(side x side) = 6(2x2) = 6(4) = 24 cm2
The surface area of a rectangular prism with length 5 cm, width 3 cm, and height 4 cm.
What is 94 cm² ?
The workers at a candy factory have been tasked with finding out how much material is required to cover the factory's famous candy bar. The candy bar measures 5 inches long, 2 inches wide, and 1 inch in height. What size wrapper will be required to cover the candy bar?
*Hint: use surface area
What is 34 in2?
SA = 2(5x2) + 2(5x1) + 2(2x1)
= 2(10) + 2(5) + 2(2)
= 20 + 10 + 4
= 34 in2
A vertex is a point where two or more line segments meet (aka corners of the 3D shape). They are called this when there are more than one.
What are vertices?
The area of this 2D shape is found by multiplying the shapes base by its height. Sometimes, this is also called length and width.
What is a rectangle?
The surface area of a cube with side lengths measuring 5 cm is equal to this.
What is 150 cm2 ?
How:
SA of a cube = 6(side x side) = 6(5x5) = 6(25) = 150 cm2
The surface area of a rectangular prism with length 8 m, width 6 m, and height 10 m.
What is 376 m² ?
Chloe is wrapping a present in a box for her friend. The top and bottom of the box measures 8 cm by 3 cm and the height of the box is 2 cm. How much wrapping paper would Chole need to cover the box (not counting any overlap)?
What is 92 cm2?
Remember:
SA = 2(8x3) + 2(8x2) + 2(3x2)
= 2(24) + 2(16) + 2(6)
= 48 + 31 + 12
= 92 cm2
An edge is a line segment joining one vertex (corner) to another. A rectangular prism has this many edges.
What are 12?
The area of this 2D shape is found by taking half of the base times the height, as it is half of a rectangle.
What is a triangle?
The surface area of a cube with side lengths measuring 10 cm is equal to this.
What is 600 cm2 ?
How:
SA of a cube = 6(side x side) = 6(10x10) = 6(100) = 600 cm2
The surface area of a rectangular prism with length 12 cm, width 9 cm, and height 7 cm.
What is 510 cm² ?
The amount of wrapping paper needed to wrap a gift box with dimensions length 10 cm, width 8 cm, and height 6 cm.
What is 376 cm2?
A polyhedron is a 3D solid made up of polygons. It has flat faces, straight edges, and vertices. This is NOT an example of a polyhedron.
What are cylinders?
*Cylinders have a curved face that wraps around the body of the prism (ex: think about a tin can or a drum).
Other possible answers: Spheres and Cones
The area of this 2D shape is found by squaring the radius and multiplying by pi (the make kind not the dessert...).
What is circle?
A cube that has a surface area of 216 cm2 has sides of this length.
*Hint: work backwards. The surface area is given. Divide by 6 (as there are 6 equal sides with equal areas) to get the area of one face. Remember unit one...how do you find the side length of a square given its area (and its not division!).
What is 6 cm?
How:
If the total surface area is equal to 216 cm2, working backwards we would have
SA = 6(side2)
216 = 6 (side x side)
<<divide both sides by 6 as there are 6 equal faces>>
216/6 = 36 cm2 --> the area of ONE SQUARE of the cube
To find side length of the area of a square, take the square root!
The square root of 36 is 6. Therefore the cube has side lengths of 6 cm.
The surface area of a rectangular prism with length 15 mm, width 4 mm, and height 6 mm.
What is 348 mm² ?
Tara made a rectangular fence out of burlap to go around her roses so that her dog would not get hurt. The fence was 4 ft long, 3 ft high, and 2 ft wide. Tara needed this many square feet of burlap to make the fence.
*Hint: You do not need all 6 faces to make the fence!
What is 36 ft2?
Remember:
We only need 4 faces to make the fence.
SA = 2(4x3) + 2(2x3)
= 2(12) + 2(6)
= 24 + 12
= 36 ft2
This is the main difference between a square and a cube.
What is an additional dimension (2D versus 3D)?
Note: A square is 2D and has dimensions such as length x width (or side x side). A cube is 3D and has dimensions such as length x width x height (or side x side x side).
While this is not an area formula, this is an essential relationship that must exist between the base and height of any 2D shape.
*This is especially important in isocelese triangles where we are not given a right angle.
A cube that has a surface area of 384 cm2 has sides of this length.
*Hint: work backwards. The surface area is given. Divide by 6 (as there are 6 equal sides with equal areas) to get the area of one face. Remember unit one...how do you find the side length of a square given its area (and its not division!).
What is 8 cm?
How:
If the total surface area is equal to 384 cm2, working backwards we would have
SA = 6(side2)
384 = 6 (side x side)
<<divide both sides by 6 as there are 6 equal faces>>
384/6 = 64 cm2 --> the area of ONE SQUARE of the cube
To find side length of the area of a square, take the square root!
The square root of 64 is 8. Therefore, the cube has side lengths of 8 cm.
Explain how to find the total surface area of a rectangular prism.
What is the total area of each face (side) of the rectangular prism?
You find the area of each face and add them all (get a total).
The surface area of a rectangular prism with a base area of 4cm2, a length of 2cm, and a height of 4cm.
What is a width of 2cm and SA of 40cm2 ?