Lesson 12

What is Surface Area?

Let’s cover the surfaces of some three-dimensional objects.

Problem 1

What is the surface area of this rectangular prism?

2 by 4 by 4 unit rectangular prism 

16 square units


32 square units


48 square units


64 square units

Problem 2

Which description can represent the surface area of this trunk?

Photograph of a treasure chest

The number of square inches that cover the top of the trunk.


The number of square feet that cover all the outside faces of the trunk.


The number of square inches of horizontal surface inside the trunk.


The number of cubic feet that can be packed inside the trunk.

Problem 3

Which figure has a greater surface area?

Figure A 5 cubes arranged in L shape. Figure B 5 cubes arranged in a cross shape.

Problem 4

A rectangular prism is 4 units high, 2 units wide, and 6 units long. What is its surface area in square units? Explain or show your reasoning.

Problem 5

Draw an example of each of these triangles on the grid.

  1. A right triangle with an area of 6 square units.
  2. An acute triangle with an area of 6 square units.
  3. An obtuse triangle with an area of 6 square units.
Image of a grid.
(From Unit 1, Lesson 9.)

Problem 6

Find the area of triangle \(MOQ\) in square units. Show your reasoning.

Triangle MOQ enclosed in rectangle MNPR.


(From Unit 1, Lesson 10.)

Problem 7

Find the area of this shape. Show your reasoning.

A four-sided shape on a grid, with two sides that drop 5 units as they cross 5 units and meet at a right angle, and two sides that drop two units as they cross 5 units.
(From Unit 1, Lesson 3.)