Area of a Triangle
The area of a triangle is half the area of a rectangle with the same base and height, giving the formula A = ½ × base × height. In Grade 6 Saxon Math Course 1, the height must be the perpendicular distance from the base to the opposite vertex, not the slant side. For a triangle with base 8 cm and height 5 cm: A = ½ × 8 × 5 = 20 cm². This formula works for all triangle types — acute, right, and obtuse — as long as the perpendicular height is used.
Key Concepts
New Concept The area of a triangle can be determined by finding half of the product of its base and height. $$A = \frac{1}{2}bh$$.
Why it matters Mastering the area of a triangle is a key step toward deconstructing any complex shape, from rocket fins to architectural designs. This simple formula introduces the powerful idea that geometric properties can be described and manipulated with symbolic language.
What’s next Next, you'll apply this formula to calculate the area of different types of triangles, including right triangles and those within parallelograms.
Common Questions
What is the formula for the area of a triangle?
A = ½ × base × height, where height is the perpendicular distance from the base to the opposite vertex.
Find the area of a triangle with base 8 cm and height 5 cm.
A = ½ × 8 × 5 = ½ × 40 = 20 cm².
Why is the triangle's area half the rectangle's area?
A triangle can be formed by cutting a rectangle diagonally, producing two congruent triangles — each half the rectangle's area.
Does the formula work for obtuse triangles?
Yes. Use the perpendicular height (which may fall outside the triangle for obtuse angles) and the base length.
Find the area of a triangle with base 12 m and height 7 m.
A = ½ × 12 × 7 = 42 m².