Answer:
A= 75.06 Sq Cm
Step-by-step explanation:
Please refer to the picture attached with this.
In ΔABD
AB = 8.5 , AD = 6 and say BD = x
Applying Pythagoras theorem in this triangle
Pythagoras theorem says
![a^2+b^2=c^{2}](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%3Dc%5E%7B2%7D)
where c is the side opposite to the right angle, and b and a are the other two sides of the right angled triangle.
![x^2+6^2=8.5^{2}](https://tex.z-dn.net/?f=x%5E2%2B6%5E2%3D8.5%5E%7B2%7D)
![x^2=72.25-36](https://tex.z-dn.net/?f=x%5E2%3D72.25-36)
![x^2=36.25](https://tex.z-dn.net/?f=x%5E2%3D36.25)
![x=6.02](https://tex.z-dn.net/?f=x%3D6.02)
Hence side ![a = x +19](https://tex.z-dn.net/?f=a%20%3D%20x%20%2B19)
a = 6.02+19
a = 25.02
Now we apply the formula for area of a triangle which is given as
![A=\frac{1}{2}\times b \times h](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20b%20%5Ctimes%20h)
Where b is the base , here we have base as a = 25.02
h is the height , here h = 6
Putting these values in Formula we get
![A=\frac{1}{2}\times 25.02 \times 6](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%2025.02%20%5Ctimes%206)
![A= 25.02 \times 3](https://tex.z-dn.net/?f=A%3D%2025.02%20%5Ctimes%203)
![A=75.06](https://tex.z-dn.net/?f=A%3D75.06)
Hence Area of the triangle is 75.06 sq cm