Area
Surface Area and Volume
Polyhedron
Nets
Triangles, Vocabulary and Exponents, Oh My!
100
A square has a side length of 5 inches. What is the area?
The area is 25 inches squared.
100
What is the surface area of this rectangular prism?
The surface area is 48 units2. This is true because the top and bottom are both 8 units. The left side and right side are also 8 units each. The front and back are 16 units each. When you add all six faces together 8 + 8 + 8 + 8 +16 + 16 = 48 units2.
100
What is the definition of polyhedra?
A polyhedron is a closed, three-dimensional shape with flat sides. When we have more than one polyhedron we call them polyhedra.
100
Which net will make the pentagonal pyramid? Why?
Net A is the correct net. First, it is the only net with a pentagon for a base. Secondly, it has five triangular faces, which the correct amount for this object.
100
What is the definition of area?
Area is a two-dimensional measurement using base and height. The answer to an area problem can be written with the exponent of 2, for example x2.
200
A rectangle has a base of 13 centimeters and a height of 7.5 centimeters. What is the area of the rectangle?
The area of the rectangle is 97.5 centimeters,
or 97 1/2 centimeters.
200
A. What is the surface area?
B. What is the volume?
A. The surface area is 112 units2.
The front and back are 12 units each, the left side and right side are 30 units each, the top and bottom are 14 units each; for a combined total of 112 units.
B. The volume is 60 units 3.
If you find the volume of each of the three sections and combine them you get 60 units. The tallest section is 36 units, the middle section is 16 units, and the smallest section is 8 units.
200
A. What is the difference between a triangular prism and a rectangular prism?
B. Draw a picture of each.
A. The difference between a triangular prism and rectangular prism is the shape of their bases.
B.
200
Which net is the correct one for the triangular prism?
B is the correct net. B is the only choice that has two triangular bases and three rectangular faces.
200
What is the definition of volume?
Volume is a three-dimensional measurement using
L x W x H. The answer when finding volume can be written with an exponent of 3, for example x3.
300
Find the area of the polyhedron, explain your reasoning. 
The area of the polyhedron is 28cm2. The way you find the area is by dividing the shape into a small square and a large rectangle. The small square is 2cm by 2cm, which is 4 cm2. The large rectangle is 4cm by 6cm, which is 24cm2. If you add them together, the total area is 28cm2.
300
A. What is the surface area of Box A?
B. What is the volume of Box A?
A. The surface area of Box A is 16,000 cm2.
The top and bottom of the box are each 20cm x 50cm =1,000cm2. The left side and right side are each 100cm x 20cm = 2,000cm2. The front and back are each 100cm x 50cm = 5,000cm2. When you combine all 6 faces, the total is 16,000cm2.
B. The volume of Box A is 100,000cm3.
Length x Width x Height is 20cm x 50cm x 100cm =
100,000cm3.
300
What is the difference between a pyramid and a prism?
The difference between a pyramid and prism is that a prism has 4 faces and is named by the two identical bases.
A pyramid is also named by the base but has all triangular faces that meet at one vertex.
300
Which net is the correct one for the hexagonal prism?
The 2nd net is the correct choice because it has two hexagonal bases and 6 rectangular faces.
300
What is the area of this triangle? What is the formula for finding the area of a triangle?
The area for this triangle is 30 units2. The formula for finding the area of a triangle is B x H x 1/2.
400
What is the area of the shaded region? Explain your thinking.
The area of the shaded region is 34 centimeters squared. The way to find the area of the shaded region is to first find the area of the larger rectangle, which is 8cm by 5cm. The total area of the rectangle is 40cm2. Next, you subtract the non-shaded region, which is 2cm by 3cm or 6cm2.
40cm2 - 6cm2 = 34cm2
400
A. What is the surface area of the rectangular pyramid?
A. The surface area is 96 units2.
There are four triangle faces that are each 15 units. There is also one square base that is 36 units2. When you combine the five faces together you get
(4 x 15) + 36 = 96 units2.
400
A. Which of the following are polyhedra?
B. If there are shapes that are not polyhedra list them and explain why they are not polyhedra.
A. A, B and D are polyhedra.
B. C and E are not polyhedra because they both have a curved edge.
400
Find the surface area of this net. What object will this net make?
The surface are is 112 units2.
There are two large faces that are each 32 units2, there are two more small faces that are each 16 units2, and the top and bottom are each 8 units2.
The net would make a rectangular prism.
400
What is the area of this triangle? How did you know which height to use? How did you find the base?
The area of this triangle is 84 units2.
The height I used was 8 units because it was perpendicular to the base.
To find the base, I added 6 units and 15 units to get the entire length of the bottom of the triangle.
500
A.If the side that is 6 units long is the base of this parallelogram, what is the corresponding height?
B. Why did you choose this for the height?
C. What is the area of the parallelogram?
A. The corresponding height for the parallelogram is 4 units.
B. This height that is 4 units is correct because it is perpendicular to the base, which means it makes a right angle.
C. The area of the parallelogram is 4units by 6 units, which equals 24units2.
500
Which rectangular prism has a larger volume? How much larger?
A.
B.
Rectangular prism B is larger by 21,750mm3.
Box A is 36,000mm3, while Box B is 57,750mm3.
57,750mm3 - 36,000mm3 = 21,750mm3
500
Name all of the polyhedra.
1. Cube (can also be a rectangular prism)
2. Rectangular prism
3. rectangular pyramid
4. triangular pyramid
5. triangular prism
500
What is the surface area of this net? What object will be made?
The surface area of this net is 48cm2.
Each triangle is 6cm2, the largest triangle is 15cm2, the middle triangle is 9cm2, and the third rectangle is 12cm2. 6 + 6 + 15 + 9 + 12 = 48
500
Solve the following problems using exponents.
A. 74 =
B. 93 =
C. 65 =
D. 132 =
A. 7x7x7x7= 2,401
B. 9x9x9 = 729
C. 6x6x6x6x6 =7,776
D. 13x13 = 169