The area of ΔIDK is 32.69 square units.
Solution:
Given data:
ID = 7 and Hypotenuse, KI = 11.67.
Let us first find KD:
Using Pythagoras theorem,
[tex]\text {Base}^{2}+\text {Height}^{2}=\text {Hypotenuse}^{2}[/tex]
[tex]ID^2 + KD^2 = KI^2[/tex]
[tex]7^2 + KD^2 = (11.67)^2[/tex]
[tex]49 + KD^2 = 136.1889[/tex]
Subtract 49 from both sides.
[tex]KD^2=87.1889[/tex]
Taking square root on both sides, we get
KD = 9.34
Area of the triangle = [tex]\frac{1}{2}\times\text{base}\times\text{height}[/tex]
[tex]$=\frac{1}{2}\times{7}\times{9.34}[/tex]
= 32.69
The area of ΔIDK is 32.69 square units.
