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19 Jun 2011, 08:51
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Recently I came across one problem solving question on gmatclub and to solve this question I used some different formula for computing area of triangle. Then I realized that many people are not aware that such formulae exist. Hence, I decided to write this post. In this post I am writing some formulae to calculate area of the triangle. If any formula left out please add it in the post.
1. Area of triangle = \(\frac{1}{2}*Base* Height\) …….. most common formula
2. Area of triangle = \(\sqrt{s(s-a)(s-b)(s-c)}\)
In the above equation S = Semi perimeter = \(\frac{(a+b+c)}{2}\)
and a=side infront of angle A, b=side infront of angle B, and c=side infront of angle C
4.jpg [ 20.12 KiB | Viewed 2887 times ]
3. Area of triangle = \(r*S\)
….. where S = Semi perimeter and r = in radius i.e. radius of the inscribed circle
4. Area of triangle = \(\frac{abc}{4R}\)
……..where a,b,and c are sides of the triangle and R = circum radius i.e. radius of the Circumscribing circle
5. Area of triangle = \(\frac{1}{2}\)* product of 2 sides * sine of included angle
6. Area of Isosceles Triangle = \(\frac{a}{4}\sqrt{4c^2-a^2}\)
7. Area of equilateral triangle = \(\sqrt{3}\) / 4 *\(side^2\)
8. Area of triangle (co-ordinate geometry)=
2.jpg [ 28.57 KiB | Viewed 2875 times ]
1. Area of triangle = \(\frac{1}{2}*Base* Height\) …….. most common formula
2. Area of triangle = \(\sqrt{s(s-a)(s-b)(s-c)}\)
In the above equation S = Semi perimeter = \(\frac{(a+b+c)}{2}\)
and a=side infront of angle A, b=side infront of angle B, and c=side infront of angle C
Attachment:
4.jpg [ 20.12 KiB | Viewed 2887 times ]
3. Area of triangle = \(r*S\)
….. where S = Semi perimeter and r = in radius i.e. radius of the inscribed circle
4. Area of triangle = \(\frac{abc}{4R}\)
……..where a,b,and c are sides of the triangle and R = circum radius i.e. radius of the Circumscribing circle
5. Area of triangle = \(\frac{1}{2}\)* product of 2 sides * sine of included angle
6. Area of Isosceles Triangle = \(\frac{a}{4}\sqrt{4c^2-a^2}\)
7. Area of equilateral triangle = \(\sqrt{3}\) / 4 *\(side^2\)
8. Area of triangle (co-ordinate geometry)=
Attachment:
2.jpg [ 28.57 KiB | Viewed 2875 times ]
20 Jun 2011, 04:10
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Thank you vyassaptarashi for your effort! However, IMO, there is a very low possibility that we would be in a position to use most of these formulae (number 2, 3, 4, and 5; possibly 6 also). Most of the GMAT problems doesn't require to have a tight grasp of all these formulae. Please, don't get me wrong; I am not demeaning you, at all.
Having said these, the formula#8 is the best take-away for me from this post. Kudo for that!
Having said these, the formula#8 is the best take-away for me from this post. Kudo for that!
20 Jun 2011, 08:42
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Schawjibb
Well, these formulae are particularly important in Data Sufficiency questions, when u know these formulae and relevant information is given then u can directly reach to the conclusion that data given is sufficient. But if u dont have information regarding such formulaes then u will spend time in using the information and looking for whether it is giving answer. All the formulae are meant not only for solving the questions but also for speeding up the calculations. They give easy approach to the question.
Also, particularly when u are scoring high on the quant section u will get conceptual questions, in that cases formulae 3,4,5, and 8 are particularly important.
