Write a mathematical expression for the area of the triangle as a function of the length of the base. use the letter s to represent the length of the base of the triangle described below. the base of an isosceles triangle is one eighth as long as the two equal sides.

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:

The given parameter can be represented as:

See attachment for illustration; where h represents the height of the triangle.

Next, we calculate the height of the triangle using Pythagoras theorem

Collect like terms

Take LCM

Take square roots of both sides

The area of the triangle is then calculated using:

So, we have:

Hence, the mathematical expression for the area of the triangle is:

Read more about areas of triangles at:

link

  A = s²√15.9375

Step-by-step explanation:

An altitude of the triangle divides it into two right triangles, each with a leg of s/2 and a hypotenuse of 8s. Then the length of the altitude (h) is given by the Pythagorean theorem as ...

  h² + (s/2)² = (8s)²

  h = s√(64 -1/4) . . . . . . . subtract s²/4 and take the square root

Then the area is ...

  A = (1/2)sh = (s/2)(s√63.75)

We can put all the constants in one place to get ...

  A = s²√15.9375

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step-by-step explanation: