What is Surface Area?

Warmup


Activity #1

Introduce Surface Area of a Rectangular Prism(Cuboid).

A Prism is a solid shape that is bound on all its sides by plane faces. There are two types of faces in a prism; the top and bottom faces are identical and are called bases. A prism is named after the shape of these bases. For example, if a prism has a triangular base it is called a triangular prism. If a prism has a rectangular base it is called a rectangular prism. In this activity, you are going to discover how the surface area of a prism is found. Just follow the instructions below.

  • Take a few minutes to interact with the rectangular prism shown here.
  • After doing so, create one that has a length = 5 units, width = 4 units, and height = 3 units. ​
  •  Move the CREATE NET to the right to see how Surface Area occurs as a net (envelope). ​
  •  Interact more with the sliders to understand Surface Area. ​
  •  Move the OPTIONS slider through three different steps to see the three sets of faces whose area is added.

Activity #2

 Find Surface Area by Examining the NET Structure.

The Net structure of a solid figure can be used to find the surface area. Follow the instructions below to find out how.

  • Check the “Show/Hide net” box.
  • Check the “Show/Hide surface area” box to see the surface area of a unit cube. Note how Surface Area can be found from the net structure.
  •  Move the “length” slider to see the effect on the figure and the surface area.
  • Repeat same with the “width” and “height” sliders.

Activity #3

 Draw Polygon with a Given Area.

The simplest polygon is the triangle. in this activity, you are going to practice drawing a triangle when the area is given.

  • Draw an example of a right triangle with an area of 6 square units.
  • Draw an example of an Acute triangle with an area of 6 square units.
  • Draw an example of an Obtuse triangle with an area of 6 square units.

Challenge #1


Challenge #2


Challenge #3

Adjust the dimensions of the rectangular prism shown below to create one with the given surface area.

  1. The edge lengths of this prism are positive integers ranging from 1 to 9.​
  2. A prism having LENGTH = 4, WIDTH = 5, and HEIGHT = 6 is equivalent to a prism having LENGTH = 6, WIDTH = 4, and HEIGHT = 5.