Question

if the height of the triangle is root 3 times of its base then find a polynomial which represents the area of triangle

Answer 1

To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram.

Answer 2

Solution:

The required polynomial is given by $A=\frac{\sqrt3}{2}b^2$

Explanation:

Let us suppose the height of the triangle is h and the base is b.

Now, we have been given that the height of the triangle is root 3 times of its base. Hence, we have

$h=\sqrt3 b$

Now, we know that the area of the triangle is given by

$A=\frac{1}{2} bh$

On substituting the value of h, we get

$A=\frac{1}{2}\times b \sqrt3\cdot b \\\\A=\frac{\sqrt3}{2}b^2$

Therefore, the required polynomial is given by

$A=\frac{\sqrt3}{2}b^2$