Answer:
Exact area = \(8\sqrt{30} \ \text{cm}^2\)
Approximate area = 43.817805 square cm
Explanation
The three sides of the triangle are
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(16853)
area = sqrt(1920)
area = sqrt(6430)
area = sqrt(64)sqrt(30)
area = 8sqrt(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 \(\text{cm}^2\)
Round the approximate decimal value however your teacher instructs.