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.
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
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.
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.
Licence
This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Video
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Starter quiz
6 Questions
Square -
Area = $$l^2$$
Triangle -
Area = $$\frac{bh}{2}$$
Parallelogram -
Area = $$b\times h$$
Trapezium -
Area = $$\frac{1}{2}(a + b)h$$
Circle -
Area = $$\pi\times r^2$$
Area = 15 cm$$^2$$ -
A triangle with perpendicular height = 5 cm and base = 6 cm
Area = 40 cm$$^2$$ -
A triangle with perpendicular height = 10 cm and base = 8 cm
Area = 6 cm$$^2$$ -
A triangle with perpendicular height = 3 cm and base = 4 cm
Area = 2 cm$$^2$$ -
A triangle with perpendicular height = 2 cm and base = 2 cm
Exit quiz
6 Questions
Area = 45 cm$$^2$$ -
A triangle with perpendicular height = 10 cm and base = 9 cm
Area = 9 cm$$^2$$ -
A triangle with perpendicular height = 6 cm and base = 3 cm
Area = 1 cm$$^2$$ -
A triangle with perpendicular height = 1 cm and base = 2 cm
Area = 2 cm$$^2$$ -
A triangle with perpendicular height = 2 cm and base = 2 cm
23.0 cm$$^2$$ -
The adjacent lengths are 7 cm and 9 cm with a 47° angle in between.
26.3 cm$$^2$$ -
The adjacent lengths are 12 cm and 6 cm with a 47° angle in between.
6 cm$$^2$$ -
The adjacent lengths are 3 cm and 4 cm with a 90° angle in between.
2.4 cm$$^2$$ -
The adjacent lengths are 1 cm and 6 cm with a 53° angle in between.
$$9\sqrt{3} \;$$ cm$$^2$$ -
The adjacent lengths are 6 cm and 6 cm with a 60° angle in between.