Geometry

Find the area of the triangles in square centimeters:

a. 3.5, 4.8, 6.1

b. 10.2, 4.4, 7.1

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  1. I will do the 1st one
    you do the 2nd

    method 1. check to see if it is right -angled, then it would be real easy
    is 3.5^ + 4.8^2 = 6.1^2 ? , NO
    --- so forget that method

    method 2:
    find the angle opposite the smallest side using the cosine law
    3.5^2 = 4.8^2 + 6.1^2 - 2(4.8)(6.1)cosØ
    cosØ = .819672..
    Ø = 34.948°
    then area = (1/2)(4.8)(6.1)sin 34.948°
    = appr. 8.386

    Method 3.
    Heron's Formula
    (If a, b, and c are the three sides and s = (1/2) perimeter, then
    Area = √( s(s-a)(s-b)(s-c) )

    s = (1/2) (3.5+4.8+6.1) = 7.2
    s-a = 3.7
    s-b = 2.4
    s-c = 1.1

    A = √(7.2x3.7x2.4x1.1) = appr 8.386

    same as method 2 answer

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  2. Use Heron's formula.
    Let a, b and c be the sides of a triangle.
    Let s = a + b + c
    Therefore the area of triangle can be calculated using this formula:
    A = sqrt[ (s)(s-a)(s-b)(s-c) ]

    It should be a little easy using this formula, so I guess you can do it on your own. :)
    Hope this helps :3

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