The area of a triangle - Higher
The area of any triangle can be calculated using the formula:
\(\text{Area of a triangle} = \frac{1}{2} ab \sin{C}\)
To calculate the area of any triangle the lengths of two sides and the angle in between are required.
Example
Calculate the area of the triangle. Give the answer to 3 significant figures.
Use the formula:
\(\text{area of a triangle} = \frac{1}{2} bc \sin{A}\)
\(\text{area} = \frac{1}{2} \times 7.1 \times 5.2 \sin{42}\)
area = 12.4 cm2
It may be necessary to rearrange the formula if the area of the triangle is given and a length or an angle is to be calculated.
Question
The area of the triangle is 5.45 cm2. Calculate the size of the acute angle YXZ. Give the answer to the nearest degree.
Use the formula:
\(\text{area of a triangle} = \frac{1}{2} ab \sin{C}\)
\(5.45 = \frac{1}{2} \times 5.3 \times 3.2 \sin{C}\)
\(5.45 = 8.48 \sin{C}\)
Rearrange the equation to make \(\sin{C}\) the subject.
Divide both sides by 8.48.
\(\sin{C} = 0.642688 \dotsc\). Do not round this answer yet.
To calculate the angle use the inverse \(\sin\) button on the calculator (\(\sin^{-1}\)).
C = 40°
The angle YXZ is 40°.
More guides on this topic
- NEW: Angles
- NEW: Angles in parallel lines
- NEW: Polygons
- NEW: Line and rotational symmetry
- NEW: Constructing triangles
- NEW: Ruler and compass constructions
- NEW: Loci
- NEW: Bearings
- NEW: Perimeter
- NEW: Area
- NEW: Volume of a prism
- NEW: Surface area of a prism
- NEW: Pyramids, cones and spheres
- NEW: Nets, plans and elevations
- NEW: Circumference and arc length
- NEW: Area of circles and sectors
- NEW: Higher – Calculating angles using circles
- NEW: Higher – Using the alternate segment theorem, tangents and chords
- NEW: Reflection
- NEW: Rotation
- NEW: Translation
- NEW: Enlargement
- NEW: Higher − Negative enlargements
- NEW: Higher – Combined transformations and invariant points
- NEW: Congruent and similar shapes
- NEW: Higher – Similarity in 2D and 3D shapes
- NEW: Pythagoras' theorem
- NEW: Solving 2D and 3D problems using Pythagoras' theorem
- NEW: Right-angled trigonometry
- NEW: Higher – Sine rule
- Angles, lines and polygons - AQA
- Loci and constructions - AQA
- 2-dimensional shapes - AQA
- 3-dimensional shapes - AQA
- Circles, sectors and arcs - AQA
- Circle theorems - Higher - AQA
- Transformations - AQA
- Pythagoras' theorem - AQA
- Units of measure - AQA
- Vectors - AQA
