Areas of States - Estimation


Janice C. Harvey

 Carver Middle School

 801 E. 133rd Place



 (773) 535-5655




Students will learn how to use the formulas for measuring the area of simple geometric shapes to estimate the area of an irregular shape.  Students will learn how to estimate the area of the states using the formulas for the areas of rectangles, squares and triangles. This lesson is designed for seventh and eighth grade students.




Each team will need these materials. (Students will work in pairs.)


·       Outline maps of individual states with distance scales.

·       Rulers

·       Calculators

·       Pencils

·       Paper

·       List of areas of all 50 states 




Review the formulas for finding the areas of rectangles, squares, and triangles. Remind students that in real life measurement situations, it is often easier to use estimation. Choose an irregularly shaped, flat object or draw an irregular shape on the board. Demonstrate to the students how the shape can be divided into sections. Approximate each section with a rectangle, square or triangle.


These formulas may be used:


o      Area of a rectangle =length ´ width

o      Area of a triangle = 1/2 ´  (base) ´  (height)

o      Area of a square = (side)2                                                                                                                     


Have students, working in pairs, choose a state and estimate the area of that state by using different shapes. They may estimate the area of the state by using the formulas for finding the area of the various shapes, and by referring to the scales on the maps.


Performance Assessment:


As a performance assessment for this lesson, give each student an outline map of a state to estimate the area of that state. Student’s final estimation should be within an 80% accuracy range.




By using the formulas measuring the areas of simple geometric shapes and the map scales, the students will be able to estimate the land area of certain states.




·        Ready to Go US Outline Maps [Scholastic Professional Books – 2000]


·       Passport to Algebra and Geometry [McDougal-Littell 1999], pp. 192-193


·       Road Atlas [Rand McNally 2000]