The area of any triangle
I can derive the formula for the area of any triangle.
The area of any triangle
I can derive the formula for the area of any triangle.
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Lesson details
Key learning points
- The formula for the area of a right-angled triangle is 0.5 x base x perpendicular height
- With an equilateral or isosceles triangle, you can use Pythagoras' theorem to find the height
- If you know one of the base angles, you can use the sine ratio to find the perpendicular height
- Doing this leads to the formula 0.5absinC
Keywords
Area - The area is the size of the surface and states the number of unit squares needed to completely cover that surface.
Sine function - The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.
Common misconception
Using any two side lengths for the sine formula.
It must be two side lengths and the angle between them. So any two side lengths of the triangle can be used so long as you also use the angle between them.
To help you plan your year 11 maths lesson on: The area of any triangle, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: The area of any triangle, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
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Explore more key stage 4 maths lessons from the Non right-angled trigonometry unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
Starter quiz
6 Questions
Area =
Area =
Area =
Area =
Area =
A triangle with perpendicular height = 5 cm and base = 6 cm
A triangle with perpendicular height = 10 cm and base = 8 cm
A triangle with perpendicular height = 3 cm and base = 4 cm
A triangle with perpendicular height = 2 cm and base = 2 cm
Exit quiz
6 Questions
A triangle with perpendicular height = 10 cm and base = 9 cm
A triangle with perpendicular height = 6 cm and base = 3 cm
A triangle with perpendicular height = 1 cm and base = 2 cm
A triangle with perpendicular height = 2 cm and base = 2 cm
The adjacent lengths are 7 cm and 9 cm with a 47° angle in between.
The adjacent lengths are 12 cm and 6 cm with a 47° angle in between.
The adjacent lengths are 3 cm and 4 cm with a 90° angle in between.
The adjacent lengths are 1 cm and 6 cm with a 53° angle in between.
The adjacent lengths are 6 cm and 6 cm with a 60° angle in between.