Question

A triangle has a base 6cm and has the same area as a circle of radius 6cm. The altitude of the triangle in cm is ….

Answer 1

Hint:
Here we have an area of a triangle which is equal to the area of the circle. And it is given that the measurement of the radius is 6cm and its altitude is also equal to 6cm . As we know that area of triangle is $\dfrac{1}{2}base\times height=\dfrac{1}{2}\times b\times h$ where b is for base and h is for height and the area of circle is $\pi {{r}^{2}}$ where r is the radius of the circle.

Complete step by step solution:
It is given that area of triangle is equal to the area of circle and length of base is 6cm and length of radius is also 6cm
Let's proceed to step 1 by just calculating the area of the triangle.
Let’s suppose altitude or height of triangle is h
Step 1: Area of triangle = $\dfrac{1}{2}\times base\times height$
 = $\dfrac{1}{2}\times 6\times h\,{{m}^{2}}$
 = $3h\,{{m}^{2}}$……………………………….(1)
Now we are calculating the area of circle which is only depend on radius r
Area of circle = $\pi {{r}^{2}}$
 =$\dfrac{1}{2}\times {{6}^{2}}\,\,{{m}^{2}}$…………………………(2)
From equation 1 and equation 2 we get
Step 2: Area of triangle = area of circle
$\dfrac{1}{2}\times 6\times altitude=\pi \times {{6}^{2}}$
$altitude =2\pi \times 6\,m$
= $12\pi \,m$
Hence the altitude of the given triangle is $12\pi $

Note:
First note that altitude and height for the triangle are the same while we are calculating the area. Altitude is the line from the vertex to the opposite side which is perpendicular to it.