Question

area of a quadrilateral = ½ length of a diagonal + sum of the length of the perpendicular from the remaining two vertices on the diagonal how it is false​

Answer 1

Answer:

Step1: lets diagonally cut the quadrilateral into two triangles.

Now let us define diagonal as ‘d’

Length of perpendicular from other vertices as h1 and h2.

Step2:

So now we have two triangles with base ‘d’ and height h1&h2 respectively.(h1 &h2 are the perpendicular distance from both vertices to diagonal)

So the area of quadrilateral(A) would be sum of the area of both triangles.(A1&A2)

Step3:

We have the formula for the area of triangle =1/2*(base)*(height)

In our case, it would be

A1=1/2*d*h1

A2=1/2*d*h2

So area of quadrilateral=A1+A2=1/2*d*h1+ 1/2*d*h2

=1/2*d*(h1+h2)