Question

Find the area of the triangles in square centimeters:

a. 3.5, 4.8, 6.1

b. 10.2, 4.4, 7.1

Answer 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

Answer 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