Area of Triangles

Students often know how to calculate the area of a rectangle and sometimes think that this formula applies to all shapes. Students explore the relationship between the area of a rectangle and the area of a triangle.

Teacher notes

• Students estimate the area of a given triangle.
• Students choose an edge of the triangle as the base, then slide a 'height line' to the correct position to identify the height.
• A rectangle with the same base and height dimensions as the triangle is drawn around the triangle. The triangle is duplicated and students then cut and fit the second triangle into the rectangle with the original triangle to determine that the area of a triangle is equal to half the area of a rectangle. They select the correct formula: Area = Ω Base X Height.
• Students enter the dimensions of the triangle into the formula to calculating its area. Where the dimensions are difficult to determine from the underlying grid, they are provided. Students will require a calculator for some of the calculations.
• The height line provided reinforces the concept that the height is perpendicular to the base and intersects with the vertex (highest point of the triangle) opposite the base.
• Scaffolding reinforces the idea that the area of a triangle is calculated as half the base times the height.
• This series could be used to investigate the conservation of area regardless of which base and height pair is chosen.

Learning objects

 Area of triangles: Triangles with a right angleStudents work with triangles with a horizontal or vertical edge. When students select the base, they are prompted that horizontal and vertical sides are easier to use for the base. Area of triangles: height intersects with the base inside the triangleStudents work with triangles that have either a vertical or horizontal side and where the height line falls within the base of the triangle. Area of triangles: height intersects with the base outside the triangleStudents work with triangles with a vertical or horizontal side, where the height line may fall outside the base of the triangle. Students fit the two triangles into the rectangle, then they must also fit in the part of the original triangle that falls outside the rectangle. Area of triangles: Triangles without vertical or horizontal sidesStudents work with triangles where none of the sides are vertical or horizontal. Area of trianglesThis is an aggregate of the other learning objects except for triangles with a right angle. Students can select the type of triangle they work with.