4 Strategies to Teach Composite Shapes

Calculating the area of composite figures and shapes is an important skill for middle school math students.  Some students will pick up on this skill quickly, and others will need various methods taught to them so they understand.  Read on to learn how to teach and challenge ALL OF YOUR STUDENTS to make sense of area of irregular shapes. 

Review:  Review how to calculate the area of shapes such as triangles and rectangles.  Make sure that students understand that height and base must be perpendicular. 

Divide:  Divide the area up into different triangles and rectangles (or parallelograms).  Students will often have different ways to divide up the composite shape.  Let them divide it up differently and compare answers. 

Negative Area:  Composite area can also be determined by taking a larger area and taking away a negative area (an area that is not actually part of the composite shape).  Take a look at the image below.  To determine the area of the L-shaped blue section, a student can determine the area of the larger square (blue) and take away the away of the negative smaller square (yellow).  This method is good to at least show to students as it will be a good skill for them to understand as they progress in mathematics. 
large blue square minus a smaller yellow square equals the area of a L shape inside a square

Problem Solving:  I ALWAYS try and incorporate problem-solving into any lesson.  With composite figures, provide shapes with sides that are not marked, but can be determined by problem-solving.  Compare Figure A and Figure B below.  To determine the area of the composite figure below, most students will determine the area of the 6 x 7 rectangle and the additional triangle.  Notice in Figure A that all dimensions to determine the area of the rectangle and triangle are given.  In Figure B the height of the triangle is not as clear.  Students would have to problem solve that the perpendicular height of the triangle is 10 - 7 = 3.  This is also a way to differentiate in your classroom.  Some students may be ready to problem-solve quicker than other students, and that is ok. 

Composite shapes with dimensions

If you are looking for a fun way to practice composite area in your classroom take a look at this fun activity  This area of composite figures worksheet is an engaging activity which includes two versions.  One version has all the measurements listed.  The other versions has missing measurements that can be determined through problem-solving.

Area of Composite Figures Activity


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