How to explain it
At this standard, students find the area of composite two-dimensional figures by decomposition, and the volume and surface area of solids built from right prisms, by breaking each figure into familiar shapes and combining the parts.
The anchor students hold onto: Decompose into shapes you know, find each part, then ADD. Subtract any removed region. For volume, add the prism volumes; for surface area, add only the faces that are exposed.
Decomposing composite figures prepares students for 8.G.C.9, the volume of cylinders, cones, and spheres, and the area and volume reasoning used throughout high school geometry.
Worked examples
Example 1
L-Shape Area
L-shape: 8 by 6, notch 4 by 3
Step 1Split the L into two rectangles.
Step 2Bottom rectangle: 8 x 3 = 24 square units.
Step 3Top rectangle: 4 x 3 = 12 square units.
Step 4Add: 24 + 12 = 36 square units.
Answer36 square units.
Example 2
Prism Volume
Two stacked boxes, find volume
Step 1Volume of a prism = base area x height.
Step 2Lower box: 5 x 3 x 2 = 30 cubic units.
Step 3Upper box: 5 x 3 x 4 = 60 cubic units.
Step 4Add: 30 + 60 = 90 cubic units.
Answer90 cubic units.
Common mistakes
What students write
Adding up all the side lengths and calling that the area, instead of decomposing and using area formulas.
The fix
Area is not perimeter. Decompose the figure into rectangles and triangles, use A = l x w and A = 1/2 b h on each piece, then add the AREAS together.
Try this
A figure is a 10 cm by 6 cm rectangle with a 3 cm by 2 cm rectangle removed. Rivera says: "The area is 10 x 6 x 3 x 2 = 360 square centimeters." Identify Rivera’s error and find the correct area.
What students write
Counting all six faces of every prism when two solids are joined face to face.
The fix
Where two solids meet, the touching faces are hidden and are NOT part of the surface area. Count only the faces you could see or touch from the outside.
Try this
Two cubes are glued face to face to make one solid. Each cube has 6 faces. Tran says: "The surface area shows 12 faces." Identify Tran’s error and find how many faces actually show.
Teacher tip
Head off the two predictable errors before they happen. First: Area is not perimeter. Decompose the figure into rectangles and triangles, use A = l x w and A = 1/2 b h on each piece, then add the AREAS together. Second: Where two solids meet, the touching faces are hidden and are NOT part of the surface area. Count only the faces you could see or touch from the outside.