What is the Area of a Triangle What is the Area of a Triangle The area of plane figures is the measure of the surface enclosed by its boundary. Now the question is that What is the Area of a Triangle, the area of a triangle or a polygon is the measure of the surface enclosed by its sides. A polygon that has three sides called the triangle. Area is measured in square units such as square centimeters and square meters, written as cm2 and m 2 respectively. Area of triangle = 1 / 2 * base * corresponding height. Any side of triangle may be taken as its base; the length of perpendicular from the opposite vertex to the base is the corresponding altitude (height). Hero's formula: - let a, b, and c the length of the sides of a triangle ABC Area of ABC = ?ABC = √(s (s – a) (s – b) (s - c)) sq units In an equilateral triangle of side a, we have
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Area = (√3 / 4 a2) For an isosceles ?ABC in which AB = AC = a and BC = b, we have Area = (¼ b √4a2 – b2 ) sq units Note : - The base and height of the triangle must be perpendicular. We can find the area of triangle by many ways like if we know the base and height, then we will use the half base time height method. If we know all three sides then we will use the hero's formula. If we know the two sides and one included angle, then we will use the side angle side method. Some examples of are of triangle are : Example 1:- Determine the area of triangle when we have base of 17 cm and a altitude of 6 cm. Solution : - Area = 1 / 2 (b * h) After putting the values of base and height. Then we get, Area = 1 / 2 (17 * 6) =1 / 2 (102) = 51 cm 2
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Example 2: - Determine the area of a triangle when you have to given a base of 8 meters and a height of 11 meters. Solution : - Area = 1 / 2 (b * h) After putting the values of base and height. Then we get, Area = 1 / 2 (8 * 11) =1 / 2 (88) = 44 cm 2 Example 3 : - Determine the area of a triangle when we have two sides 3 cm, 6 cm and in the between angle is 30 degree. Solution : - Area = (ab sin C)/2 = (3 * 6 sin 30)/2 = (18 * 0.5)/2 = (9) / 2 = 4.5 cm 2 We have seven ways by which we can solve the area of triangle . Three of them we have discussed and the remaining four are below Area = a2 * sin (B) * sin (c) / (2 * sin (B + C)) Area = f * g / 2- v* w /2 Area = = abs((xB * yA – xA * yB) + (xC * yB – xB* yC) + (xA * yC – xC* yA)) / 2
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