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Which of the following figures has the largest area?
I. A circle of radius
II. An equilateral triangle whose sides each have length 4
III. A triangle whose sides have lengths 3, 4 and 5
I
II
III
I and III
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3 Answers
69Area of the equilateral triangle - √3 * side24 = √3 * 42 4 = 4√3 = 6.92820....
Area of the scalene triangle (by Heron's formula)
= √s(s-a)(s-b)(d-c) where s= semiperimeter = (a+b+c)/2 and a, b, c are the three sides
Therefore, area = √6*3*2*1 = √36 = 6
However, this triangle is a right triangle. So, you can solve it by the formula (Base * Altitude)/2 where Base = 3 or 4 and Altitude = 4 or 3. In all the cases, the answer is same.
So, Area of Equilateral Triangle > Area of Scalene Triangle.
