Understanding triangle area calculation is crucial in geometry. This overview covers formulas for oblique triangles using sine, simplified methods for right-angled triangles, and height determination in equilateral triangles. It emphasizes the use of the base-height formula, the Law of Sines, and the Pythagorean theorem to solve various triangle area problems.
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In right-angled triangles, the area can be calculated using the formula area = ½ × base × height, with the base and height being the two legs that form the right angle
The Pythagorean theorem is used to find missing side lengths in right-angled triangles, with the equation being a² + b² = c²
The height of an equilateral triangle can be found by constructing a perpendicular line from a vertex to the midpoint of the opposite side and using the Pythagorean theorem
Once the height is known, it can be substituted into the general area formula to calculate the area of an equilateral triangle
00
For the area calculation to be correct, the base and height must meet at a ______ angle.
right
01
Formula for area of oblique triangle
Area = 1/2 × a × b × sin(C), where a and b are sides, C is included angle
02
Law of Sines relation to oblique triangle area
Area formula derived from Law of Sines, used when height is not perpendicular
