Kinds of triangle and their area

This lesson asks you to identify properties of triangles and build different kinds, and to use area relationships to develop the area formula for a triangle. The museum offers one chapter that names three kinds of triangle and gives the area of a triangle with a worked example. Building triangles from measurements, parallelograms and your own development of the formulas are for your class to bring. ¹

Draw a triangle of each kind and look at its angles. Say what you see that sets each kind apart.

Cut or fold a rectangle or parallelogram to make a triangle. Explain how the two areas are related.

The chapter on measuring in al-Khwarizmi's book says triangles are of three kinds, right, acute and obtuse. It works one example, an acute triangle of unequal sides of 13, 14 and 15 cubits: the height is found by al-jabr and al-muqabala, giving a height of twelve and an area of eighty-four ^{2 3}. The record on mensuration gives the chapter's rule: the area of a triangle is its height times half its base ⁴.

In al-Khwarizmi's example the height is twelve, the area is eighty-four, and the sides are 13, 14 and 15. Which side do you think was the base, and why?

• Mensuration: the chapter's triangles and their areas.
• The Book of al-Jabr and al-Muqabala: the book that holds the chapter.
• Al-Khwarizmi: the author of the book.

Read about mensuration in al-Khwarizmi's book. Draw a triangle, measure its base and height, and use the chapter's rule to find its area.