Vocabulary
What do you call any flat, 2D surface of a 3-dimensional geometric figure?
A face
Find the total surface area of a cube with a side length of 3 cm.
54 cm^2
How many total faces does a triangular prism have?
5 faces
How many triangular faces does a square pyramid have?
4
Sarah is wrapping a birthday gift shaped like a perfect cube. If the side length of the box is 5 inches, what is the minimum amount of wrapping paper she needs to cover the box completely?
150 in^2
What is the term for the straight line segment where two faces of a 3D solid meet?
An edge
What is the algebraic formula used to find the total surface area of a rectangular prism with length (l), width (w), and height (h)?
SA = 2lw + 2wh + 2lh
What two specific geometric shapes make up the faces of any triangular prism?
A rectangle and triangle
What is the total number of faces on a triangular pyramid (also known as a tetrahedron)?
A standard cereal box is 10 inches tall, 8 inches wide, and 2 inches deep. How much cardboard is required to manufacture one box, ignoring overlapping flaps?
232 in^2
What is the name of a flattened, 2D pattern that can be folded up to create a 3-dimensional shape?
A net
Find the total surface area of a rectangular prism that is 4 inches long, 2 inches wide, and 5 inches tall.
76 in^2
Find the total surface area of a right triangular prism where the triangular bases have sides of 3 cm, 4 cm, and 5 cm (with a base area of 6 cm^2). The length (height) of the prism is 10 cm.
132 cm^2
Find the total surface area of a square pyramid with a base side length of 4 inches and a slant height of 6 inches.
64 in^2
A canvas camping tent is shaped like a triangular prism (including a canvas floor). The triangular front and back doors have a base of 6 feet and a height of 4 feet (with side edges of 5 feet). The tent is 10 feet long. How much canvas fabric was used to make the entire tent?
184 ft^2
In a pyramid, what specific term describes the height of one of its triangular faces, measured from the base to the top vertex along the side?
A slant height
A standard cube has a total surface area of 150 cm^2. What is the length of just one of its edges?
5 cm
If the perimeter of a prism's triangular base is 15 cm, the area of one triangular base is 10 cm^2, and the height of the prism is 8 cm, what is its total surface area?
140 cm^2
Find the total surface area of a regular triangular pyramid if the area of its base is 15 cm^2, the perimeter of its base is 18 cm, and its slant height is 7 cm.
78 cm^2
A wooden block is shaped like a square pyramid. The bottom square base has sides of 6 cm. The triangular faces have a slant height of 8 cm. If you want to paint the entire block except for the bottom base, how many square centimeters will you end up painting?
96 cm^2
Explain the difference between lateral surface area and total surface area.
Lateral surface area is the area of all the sides excluding the base(s), while total surface area includes the area of the sides plus the base(s).
Calculate the total surface area of a large rectangular shipping container that has a length of 10 meters, a width of 3 meters, and a height of 4.5 meters.
177 m^2
A triangular prism has an equilateral triangle base with a side length of 6 cm and a triangle height of 5.2 cm. The main length of the prism is 12 cm. Find its total surface area.
247.2 cm^2
A square pyramid has a total surface area of 105 cm^2. If the area of its square base is 25 cm^2, what is the area of just one of its triangular faces?
20 cm^2
A juice box is a rectangular prism measuring 4 cm by 6 cm by 10 cm. Due to a design change, the company increases the height to 12 cm but keeps the width and length the same. By how many square centimeters does the total surface area increase?
40 cm^2