Engaging Activities for Finding the Area of a Triangle in Middle School

Use a Quadrilateral to Help

• To find the formula for a quadrilateral, multiply the measurement of the base times the measurement of the height of the polygon. Use the background knowledge of finding the area of the quadrilateral to help the students find the area of a triangle. Ask the students to draw a quadrilateral on a piece of grid paper and cut it out. They find the area of this polygon by measuring the base and height. Tell the students to turn the quadrilateral into two equal triangles. Let them experiment with folding to find the triangles. Folding in a diagonal line from vertex through the center to the opposite vertex results in two equal triangles. Ask the students to determine the formula for the area of the triangle.

Geoboards

• Provide students with geoboards and rubber bands. Ask them to make a triangle on the geoboard. The students find the area of the triangle by using a different rubber band to make a parallelogram which shares two sides with the triangle. Instruct the students to find the area of the parallelogram by counting the units within the parallelogram band. The triangle area is half of the parallelogram. Ask the students to try to make other types of triangles -- isosceles, equilateral and scalene -- and find the area.

Finding the Relationships

• Pattern blocks can be used to help students find the relationships between shapes. Pattern blocks are made up of triangles, squares, parallelograms, trapezoids, rhombuses and hexagons. Give each child a mixture of the pattern blocks. Ask them to look for the relationships between the shapes. Let them discover how two triangles completely cover the square. Six triangles cover the hexagon. As they make these discoveries ask them to find the formulas for the area of each shape. As a challenge, give the students an area measurement. Ask them to make a design using triangles and other pattern blocks to equal the area measurement provided.

Guest Speaker

• Students become more engaged when they realize how information taught in math class might be used in their lives. Ask a contractor to speak to your class about how he uses area formulas in his job. Right triangles are used in many aspects of construction. The speaker shows the students how he calculates area to help him order supplies and determine his budget. Ask the contractor to bring in a variety of tools he uses to help measure area.