Answer:
The Area of Δ ABC = 219.13
Step-by-step explanation:
The hard part about this problem is finding the area without the height
The formula to do this is Area = [tex]\sqrt{S(S-A)(S-B)(S-C)}[/tex]
A, B, C represent the sides
S represents [tex]\frac{1}{2}[/tex] (A + B + C)
In this equation, we will make the base be A, and the other two sides will be B and C
Sides B and C are the same length because they meet at a 90° angle
Lets plug the numbers into the variables
A = 28
B= 21
C= 21
Remember: S represents [tex]\frac{1}{2}[/tex] (A + B + C)
S = [tex]\frac{1}{2}[/tex] (28 + 21 + 21)
S = [tex]\frac{1}{2}[/tex] (70)
S = 35
Lets plug the numbers into the Area Formula now!
Area = [tex]\sqrt{35(35 - 28)(35 - 21)(35 - 21)}[/tex]
According to the order of operations, we need to do the calculations in parentheses first
35 - 28 = 7
35 - 21 = 14
35 - 21 = 14
14 x 14 x 7 = 1372
1372 x 35 = 48020
[tex]\sqrt{48020}[/tex] = 219.13
The Area of Δ ABC = 219.13
