SOL Objective(s):
8.11 The student will solve practical area and perimeter problems involving composite plane figures.
The Basics and Background Information
• A polygon is a simple, closed plane figure with sides that are line segments.
• The perimeter of a polygon is the distance around the figure.
• The area of any composite figure is based upon knowing how to find the area of the composite parts such as triangles and rectangles.
• The area of a rectangle is computed by multiplying the lengths of two adjacent sides ( A = lw ).
• The area of a triangle is computed by multiplying the measure of its base by the measure of its height and dividing the product by 2 (A = 1/2 bh ).
• The area of a parallelogram is computed by multiplying the measure of its base by the measure of its height ( A = bh ).
• The area of a trapezoid is computed by taking the average of the measures of the two bases and multiplying this average by the height [ A = 1/2 h(b1 + b2) ].
(Sorry for the b1 and b2. The numerals there should be subscript, but this website does not recognize sub or superscript  at least as far as I know.)
• The area of a circle is computed by multiplying Pi times the radius squared ( A =π r2 ).
• The circumference of a circle is found by multiplying Pi by the diameter or multiplying Pi by 2 times the radius (C =π d or C = 2π r ).
• An estimate of the area of a composite figure can be made by subdividing the polygon into triangles, rectangles, squares, trapezoids and semicircles, estimating their
areas, and adding the areas together.
• The perimeter of a polygon is the distance around the figure.
• The area of any composite figure is based upon knowing how to find the area of the composite parts such as triangles and rectangles.
• The area of a rectangle is computed by multiplying the lengths of two adjacent sides ( A = lw ).
• The area of a triangle is computed by multiplying the measure of its base by the measure of its height and dividing the product by 2 (A = 1/2 bh ).
• The area of a parallelogram is computed by multiplying the measure of its base by the measure of its height ( A = bh ).
• The area of a trapezoid is computed by taking the average of the measures of the two bases and multiplying this average by the height [ A = 1/2 h(b1 + b2) ].
(Sorry for the b1 and b2. The numerals there should be subscript, but this website does not recognize sub or superscript  at least as far as I know.)
• The area of a circle is computed by multiplying Pi times the radius squared ( A =π r2 ).
• The circumference of a circle is found by multiplying Pi by the diameter or multiplying Pi by 2 times the radius (C =π d or C = 2π r ).
• An estimate of the area of a composite figure can be made by subdividing the polygon into triangles, rectangles, squares, trapezoids and semicircles, estimating their
areas, and adding the areas together.
Essential Knowledge and Skills
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to...
• Subdivide a figure into triangles, rectangles, squares, trapezoids and semicircles. Estimate the area of subdivisions and combine to determine the area of the composite figure.
• Use the attributes of the subdivisions to determine the perimeter and circumference of a figure.
• Apply perimeter, circumference and area formulas to solve practical problems.
• Subdivide a figure into triangles, rectangles, squares, trapezoids and semicircles. Estimate the area of subdivisions and combine to determine the area of the composite figure.
• Use the attributes of the subdivisions to determine the perimeter and circumference of a figure.
• Apply perimeter, circumference and area formulas to solve practical problems.
Vocabulary and Things to Know:How to express units:
Perimeter and Circumference are expressed in units. Area is expressed in units squared. (...because you're measuring in TWO directions.) Volume is expressed in units cubed. (...because you're measuring in THREE directions.) Parts of shapes and variables that represent them. length base width height Perimeter (The distance or measurement around the figure.) Circumference ("Perimeter" of a circular figure.) Area Volume Composite shapes  shapes made of other shapes. Formulas  "recipes" for finding information. Formulas can be rewritten. A=1/2(bh) is the same as A=(bh)/2. Formulas for finding perimeter and area of regular shapes (Although students will have formula sheets, knowing/memorizing formulas is encouraged.) 
Be Able To:Subdivide and identify known shapes within composite shapes.
Read measurements indicated. Use formulas to find perimeter and area of shapes. Rewrite formulas. Identify parts of formulas. Substitute measurements for corresponding variables. Find area of known shapes. Calculate area of composite shapes. 
The topic: What is it and what will we learn?
When confronted with an irregular shape, "cut" it into shapes you can manage and "add up" measurements OR look at a bigger pictures and subtract measurements.
Pacific Crest Resources and DevelopmentInformation and thorough explanation with sample problems.

GlencoeInformation and thorough explanations with sample problems.

Problems Involving Composite ShapesSample problems.

Virtual Nerd.comWebsite that includes a video showing how to take shapes apart, find area, and then add areas together.

Passy's World of Mathematics 
Perimeter and Area of Composite ShapesStep 1: Find measurements of unknown shapes
Step 2: Divide composite shape into familiar shapes Step 3: Find area of all shapes and calculate area composite shape. 

Area of Composite ShapesDemonstration of how to label and calculate area of composite shapes. Notice what work is shown and what work was not shown.


Composite AreasTutorial demonstrates how to "see" four basic shapes and then to use those shapes to find the area of composite shapes. Good for seeing the overall process.


Areas of Combined Shapes or a Composite FigureFour examples are shown. The last example shows how to subtract negative space. This is an important part of the video to view.


Area of Composite FigureA sample problem is demonstrated.


Area of Composite FiguresSimpler example.


That Quiz.orgOnline practice that will tell you whether your answers are correct or not and will time your responses.
You can also make your own quiz and practice finding area, perimeter, surface area, and volume, along with lots of other mathematical practice. 