Using heron's formula,find the area of a triangle whose sides are 3mm ,7mm and 8.4mm correct to 1decimal place?

First, we need to calculate the semi-perimeter of the triangle using the formula:

s = (a + b + c) / 2
s = (3 + 7 + 8.4) / 2
s = 9.7 / 2
s = 4.85

Now, we can use Heron's formula to find the area of the triangle:

Area = √(s * (s - a) * (s - b) * (s - c))
Area = √(4.85 * (4.85 - 3) * (4.85 - 7) * (4.85 - 8.4))
Area = √(4.85 * 1.85 * -2.15 * -3.55)
Area = √(45.1278125)
Area ≈ 6.7 mm²

Therefore, the area of the triangle is approximately 6.7 mm².

Given sides of a triangle are
a= 3mm b= 7mm c=8.4mm
Semi-perimeter (s)=( a+b+c)/2
=(3+7+8.4)/2
=18.4/2
=9.2mm
Using Heron's Formula
Area (A) = √[s(s-a)(s-b)(s-c)]
= √[9.2(9.2-3)(9.2-7)(9.2-8.4)]
=√[9.2-6.2-2.2-0.8]
=√[96.4528]
= 9.82 mm2
Correct to 1 decimal place area of the triangle is 9.8mm2