The area of a triangle is the product of its base and height, divided by 2. The mathematical expression for the area of the triangle is: [tex]\frac{\sqrt{255}}{4}s^2[/tex]
The given parameter can be represented as:
[tex]Base = s[/tex]
[tex]Length = 8s[/tex]
See attachment for illustration; where h represents the height of the triangle.
Next, we calculate the height of the triangle using Pythagoras theorem
[tex](8s)^2 = h^2 + (\frac 12s)^2[/tex]
[tex]64s^2 = h^2 + \frac 14s^2[/tex]
Collect like terms
[tex]h^2 = 64s^2 -\frac 14s^2[/tex]
Take LCM
[tex]h^2 = \frac{4 \times 64 -1}{4}s^2[/tex]
[tex]h^2 = \frac{255}{4}s^2[/tex]
Take square roots of both sides
[tex]h = \sqrt{\frac{255}{4}s^2[/tex]
[tex]h = \frac{\sqrt{255}}{2}s[/tex]
The area of the triangle is then calculated using:
[tex]Area = \frac 12 \times Base \times Height[/tex]
So, we have:
[tex]Area = \frac 12 \times s \times \frac{\sqrt{255}}{2}s[/tex]
[tex]Area = \frac{\sqrt{255}}{4}s^2[/tex]
Hence, the mathematical expression for the area of the triangle is: [tex]\frac{\sqrt{255}}{4}s^2[/tex]
Read more about areas of triangles at:
https://brainly.com/question/11952845
