Answer :
Answer:
Exact area = [tex]8\sqrt{30} \ \text{cm}^2[/tex]
Approximate area = 43.817805 square cm
Explanation
The three sides of the triangle are
- a = 8
- b = 11
- c = 13
Add up the sides and divide the sum in half to get the semi-perimeter which is half the perimeter.
s = (perimeter)/2
s = (a+b+c)/2
s = (8+11+13)/2
s = 16
Now we can use Heron's Formula to find the area of this triangle.
area = sqrt(s*(s-a)*(s-b)*(s-c))
area = sqrt(16*(16-8)*(16-11)*(16-13))
area = sqrt(16*8*5*3)
area = sqrt(1920)
area = sqrt(64*30)
area = sqrt(64)*sqrt(30)
area = 8*sqrt(30) is the exact area
area = 43.817805 is the approximate area
The units for the area would be "square centimeters" abbreviated as "square cm" or [tex]\text{cm}^2[/tex]
Round the approximate decimal value however your teacher instructs.
