Surface Area and Volume

Nets of Rectangular Prisms

A pattern that you can cut and fold to make a model of a solid shape. This is a net of a rectangular prism.

Nets of Triangular Prisms

A pattern that you can cut and fold to make a model of a solid shape. This is a net of a triangular prism.

Triangular Prism: Find the Volume

The formula looks exactly the same as the one used to find the volume of a rectangular prism. Here are some key points to keep in mind. Remember that B in the formula is now the area of a triangle, not the area of a rectangle. Also notice that the h, height, is the part that connects the two triangles.

Triangular Prism: Given the Volume, Find the Missing Dimension

To find the missing dimension, start with the same formula as you would for the volume of a triangular prism, V = Bh. Remember that V is given here. So, make sure to substitute in for V like in this example's second step. Next, simplify everything you can on the right side of the equation. Then, solve for the missing dimension as this example did to find the measure of b, the base of the triangle.

Rectangular Prism: Given the Volume, Find the Missing Height

To find the missing height of a rectangular prism, you should still start with the same formula V = lwh. Make sure to substitute V, since the volume is given here. Then, solve for h, the height.

Rectangular Prism: Find the Surface Area (Net)

To find the surface area of a rectangular prism using a net, label each of the faces you will use. Remember that there is a twin for each face. Then find the area for each face using the dimensions given. Remember to double each area. Finally, add up to find the total surface area of the prism. Notice how well organized and clear each step is from top to bottom in this example.

Rectangular Prism: Find the Surface Area (prism)

To find the surface area of a rectangular prism, using the 3-D prism, make sure to find the area of each face. In this case, we find the area of the front, the top and the side. Remember to double each area since they have a twin face. Finally, add up to find the total surface area of the prism. Notice how this example starts with the formula. Then, it shows substitution and solution.

Triangular Prism: Find the Surface Area

To find the surface area of a triangular prism, you must find the area of 5 faces: 2 triangles and 3 rectangles. Notice this example organizes each face by color coding. Then, add up the area of the 5 faces to find the surface area. Remember to use square units since this is an area problem.

Rectangular Prism: Find the Volume

To find the volume of a rectangular prism, start with the formula V = lwh. Then substitute the dimensions into the formula and solve. Notice how this example converts the mixed numbers into decimals by rewriting each as an improper fraction, then dividing to get a decimal number.

Triangular Prism: Find the Volume

To find the volume of a triangular prism, start with the formula V = Bh, where B is the area of the triangular base. Remember that h is the height of the prism and is the part that connects the two triangles in the prism. Notice how this example starts with the formula. Then, it shows substitution and solution.