Measuring the surface area of irregular objects can be a challenge, especially if precise measuring tools are not available or if the object in question has a complex shape. However, there is a simple and effective method for calculating the surface area of irregular objects using a graph paper. This method involves counting the squares within the shape and using a mathematical formula to calculate the total surface area.

This measuring method is not only useful in everyday life, but also relevant in fields such as botany, where it is important to measure the surface area of plant leaves to study their physiology and response to environmental changes. Furthermore, the use of the scientific method in this experiment is essential to ensure the accuracy and reliability of the results, which is crucial in any scientific study.

In this experiment, participants are expected to learn how to calculate the surface area of irregular objects and understand the importance of the scientific method in measuring and analyzing the data obtained. The knowledge and skills acquired in this experiment can be applied in various areas of life and can be useful in future scientific studies.


In this experience, students will be able to:

  • General Objective: Foster the learning of techniques for measurement and the use of the scientific method.

  • Specific Objectives:

    1. Apply the scientific method to solve an experimental problem, focused on calculating the surface area of a plant leaf using graph paper.
    2. Develop observation, measurement, recording, and data analysis skills in executing the experiment.
    3. Use descriptive statistical tools to analyze the data obtained and draw accurate and reliable conclusions.
    4. Communicate the results of the experiment clearly and organized, using the scientific report format.


Develop a group hypothesis and write it correctly. Remember that you can see how to write a hypothesis in Spanish at: https://www.youtube.com/watch?v=2KRMhdTEuiw


  • Tree leaf.
  • Black pencil.
  • Red and green colored pencils.
  • Ruler.
  • Graph paper.


  • Draw the outline of the leaf.

  • Measure squares of 1cm x 1cm.

Superficie de una hoja: cuadrados de 1cm x 1cm

  • Color the complete squares with green and the incomplete squares with red.

Superficie de una hoja: cuadrados de 1cm x 1cm


  1. Attach the graph papers.
  2. Count the complete squares (this magnitude will be denoted as “C”). Count the incomplete squares (this magnitude will be denoted as “I”).
  3. Calculate the surface area (S) of the leaf by performing the operation: S = C + \frac{I}{2}. Remember that both C and I are measured in cm and that S is measured in cm² (why?).



Write here whether your hypotheses were correct or not.

The experiment conducted with plant leaves and graph paper has allowed participants to learn how to calculate the surfaces of irregular objects. The results obtained indicate that the method used to calculate these surfaces has been effective, as a high degree of accuracy has been achieved in the calculations performed. Additionally, it has been demonstrated that the use of simple tools such as graph paper is useful for calculating the surfaces of complex objects.

Likewise, the development of skills in the application of the scientific method for report writing has been encouraged. Participants have been able to record data clearly and orderly, perform precise calculations, and present results effectively.

Overall, the experiment has allowed for an improved understanding of mathematical concepts and encouraged the development of scientific skills in the participants. It is hoped that these skills and knowledge will be useful in their academic formation and in their everyday life.

Recursos en línea:

Here are some online sources in English that you can use to view simulations or activities for calculating the surface area of irregular objects:

  1. GeoGebra: https://www.geogebra.org/m/rgdxqr4t

This GeoGebra page has an online interactive activity that allows you to explore how to calculate the surface area of irregular objects using different methods, including the box method and Riemann approximation.

  1. Wolfram Demonstrations Project: https://demonstrations.wolfram.com/AreaOfAnIrregularShape/

This Wolfram project has a simulation that demonstrates how to calculate the surface area of irregular shapes by breaking them down into smaller regular shapes, such as rectangles or triangles.

  1. Mathigon: https://mathigon.org/course/geometry/surface-area

Mathigon is an interactive textbook that provides lessons on surface area, including how to calculate the surface area of irregular objects. The lessons include interactive examples, animations, and exercises to help you practice and understand the concepts.

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