Surface Area of Prisms Math 10-3 Ch.3 Measurement

The basics….  Most of the solid objects we are familiar with are 3-D or “3-Dimensional”. This means that these objects have length, width/depth and height.  A prism is a 3-D shape whose “bases” (or ends) are of the same size and shape and are parallel to one another.  The base shape of a prism is usually described in the name.  For example, a Triangular Prism will have a base in the shape of a triangle.  What is the base shape of a Trapezoidal Prism? Trapezoid

The basics…  Each side of a prism is called a face – a 2-D object that forms a flat surface of a 3-D object.  Imagine a gift box. We would call this a rectangular prism because the base shape is a rectangle. Now imagine you are going to wrap this gift box. The area that you wrap is called the Surface Area OR SA  The surface area of a 3-D object is the sum of all the areas of the faces of the object.

Practice Drawing 3-D Shapes  Let’s practice drawing a rectangular prism  Step 1: Draw the base shape (rectangle)  Step 2: Draw the exact same rectangle, above and slightly to the right of the original  Step 3: Connect the corners of your first rectangle and your second rectangle

Counting Faces  An easy way to count the number of faces are prism has is to visualize the net.  A net is a flattened 3-D shape; imagine a box that has been flattened out.  For example, if we flattened out this box   The net would look like this   We can now easily count the number faces. = 6 faces

Calculating Surface Area  Let’s consider the same box. Here are the dimensions of the box:  We would say the length is 5 cm, the width is 4 cm and the height is 3 cm

Calculating SA  Consider the net again:  What is the area of this piece? :  A rectangle = l x w = 5cm x 3 cm = 15 cm 2  How many sides are there like this?  2 sides  2 x 15 cm 2 = 30 cm 2

Calculating SA  What is the area of this piece? :  A rectangle = l x w = 5 cm x 4 cm = 20 cm 2  How many sides are there like this?  2 sides  2 x 20 cm 2 = 40 cm 2

Calculating SA  What is the area of this piece?:  A rectangle = l x w = 4 cm x 3 cm = 12 cm 2  How many sides are there like this?  2 sides  2 x 12 cm2 = 24 cm 2

What is the TOTAL SA?  Add up the surface area of all the pieces:  SA = 15 cm cm cm cm cm cm 2 = 94 cm 2  OR  SA = 30 cm cm cm 2 = 94 cm 2