The area is the size of the surface and states the number of unit squares needed to completely cover that surface.

The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.

The area of any triangle

Maths

In the prior unit, pupils explored the trigonometric ratios for right-angled triangles in a variety of situations. In this unit, pupils explore what can be done when we have a triangle that is not right-angled.

Non right-angled trigonometry

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

Match the areas of these triangles with their dimensions. 

A right-angled triangle has a height of 13 cm and a hypotenuse of 20 cm. The area of the triangle to 1 decimal place is {{}}cm$$^2$$.

A triangle has two adjacent lengths of 8 cm and 9 cm with an angle in between of 53°. The area of the triangle to 1 decimal place is {{}}cm$$^2$$.

Area = $$\frac{1}{2}ab\text{sin}C$$, despite a, b and C being explicit in the formula, they just mean two adjacent sides and the angle between them. Select other formulas for the area.

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.

Match the areas with the dimensions of the triangle. 

Six equilateral triangles are put together to make a regular hexagon. The length of each triangle is 6 cm. Work out the exact area of the regular hexagon. 

Match the polygon with the formula for calculating its 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 regular hexagon is made up of 6 equilateral triangles. The total area of the regular hexagon is 120 cm$$^2$$. The area of one triangle is {{}}cm$$^2$$.

A right-angled triangle has a height of 8 cm and a base of 5 cm. Work out the length of the hypotenuse to 1 decimal place.

A right-angled triangle has a height of 4 cm and a hypotenuse of 15 cm. Work out the length of the base to 1 decimal place.

A rectangle has a width of 5 cm and a diagonal length of 13 cm. The area of the rectangle is {{}}cm$$^2$$.

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