Shady Figures

7 teachers like this lesson
Print Lesson


SWBAT find the area of shaded regions by using the area formulas of triangles, rectangles, and trapezoids.

Big Idea

Making use of structure (MP7) to find the area of shaded regions!


10 minutes

The students are instructed to create their own irregular figure, assign side lengths, and solve to find the area.  Part of common core is to allow students to create their own problem.  As students are working, walk around to assess understanding of irregular figures and how to determine the area.  By students creating their own figure and assigning the side lengths, they are working with MP 1 and MP2.  Students that create figures out of triangles, rectangles, parallelograms, and trapezoids have a clear understanding of how to find the area of irregular figures.  If students are drawing random figures (not using the mentioned shapes), ask them how they would find the area.  You may ask them to get out their notes to see how we found the area of irregular shapes.  This should help them realize they need to work with shapes they know how to find the area.

Tools:  Do now problem, Shady figures notes and power point

Finding the Area of Shaded Regions

30 minutes

Students will be applying the formulas of triangles, rectangles, parallelograms and trapezoids to find the area of shaded regions.  The next leap for this lesson is to get them to see that they will need to subtract the areas to find the shaded regions.

Begin by asking students what shapes they see?  In each example, there are shapes they already know. 

Have them find the area of each shape.  Once they do this, ask them what to do if we need the total area of both shapes?  Allow students time to discuss this.

Then ask them to discuss a strategy to find the area of the shaded region? Listen for students to say they would subtract the areas to find what is left over. (SMP 4: Modeling with math.  Finding the areas and subtracting to find the shaded region)(MP7: students should notice that by subtracting the areas, the remaining part represents the shaded region.)

You can apply this questioning to each example. Students should be given time to make this connection on their own. If possible, give them a scenario for each problem.

Question 1:  A shed is placed in the yard in the shape of a square.  The rectangle yard needs sod.  How much sod is needed for the yard?

Question 2: The outdoor venue is shaped like a trapezoid.  The orchestra has a rectangular space for their instruments.  How much flooring is left over for the rest of the band?

Question 3: A tent has a triangular opening.  How much canvas does the remaining tent cover?

These are just examples.

Tools: Shady figures notes and power point


25 minutes

Students will be working in groups to solve problems that require them to subtract areas to find their solution.  They begin by working independently and then get their answers checked by a tablemate.

There are only 4 problems due to the amount of work needed to solve. Remind students to be neat with their work so someone else can check it for them.

Question 3 requires them to subtract twice.  It will be interesting to see if students recognize the corners of the rectangle form a square.  If students are able to recognize this, they have achieved an expert level of understanding of areas.

Working in the round table supports mathematical practices

SMP1: Sense-making, finding the entry point of the problem.

SMP2: Reasoning, understanding what the numbers mean.

SMP3: Arguing, Checking the work of others

SMP4: Modeling, using the formula to help them with the math



15 minutes

Students will be working on an application problem independently.  They will need to understand the problem and what they are being asked to do (MP1).  As students are working on  this problem, it will be important to see that they recognize the meaning of the 2ft path.  In their work, they should find that the dimensions of the large rectangle are 17ft x 13ft and they should subtract the area of the rectangle with the dimensions of 13ft x 9ft. 

The solution to this problem is: 104ft²

I will be collecting this as evidence of student learning.