How to Figure Out the Angle & Length to Get the Area of a Triangle

There are three types of triangles: equilateral, isosceles and scalene.

Triangles are polygons that have three points and three sides. It is one of the basic geometric shapes. The area formula for triangles is "area = 1/2 bh" with "b" meaning "base" and "h" meaning "height." Oftentimes the height and angles are not listed, but can be determined by the measurements of the triangle -- at least two side measurements are given. Then, using the law of sines from trigonometry -- an equation where the lengths of a triangle are related to the sines of it, allowing you to calculate the sides of a triangle if two angles and one side are given -- to calculate the height of a triangle, the area can be found.

Things You'll Need

• Pencil or pen
• Calculator
• Protractor

Instructions

1. Determine the type of triangle. If all three sides have equal measurements, it is an equilateral triangle, which means all three angles are 60 degrees. If two sides or angles are equal, it is an isosceles triangle. If all the sides are unequal, it is a scalene triangle.

2. Check if the triangle is a right triangle. Isosceles triangles are often right triangles (the angle measurements are 45-90-45) but scalene triangles can also have a 90-degree right angle. If it is, there will be a square drawn where two of the points on the triangle meet.

3. Label the three points of the triangle "A," "B" and "C." Label the side facing point A "a," the side facing point B "b," and the side facing point C "c."

4. Label the angle of point A "α," point B "β" and point C "γ."

5. Measure the angle of one of the points using a protractor. It is recommended to measure the angle facing a side without a measurement given. The "sin" of this angle is the height of the triangle.

6. Adjust the area formula to replace "h" in the formula (the height of the triangle) with the sin of the angle you measured. If you measured angle α, the formula will be "area = 1/2 b c sinα." If you measured angle β, the formula will be "area = 1/2 c a sinβ," and if you measured angle γ the formula will be "area = 1/2 ab sinγ."

7. Place the measurements of the triangle in the appropriate places per the formula determined in Step 5 and calculate the area.

References

• Wolfram MathWorld: Triangle Area
• Clark University: Laws of Cosines and Sines