Question

Graph the quadrilateral ABCD with A(-5,8), B(7,4), C(-5,0), and D(-9,4), and then find its area?

Answer 1

This is a kite with diameters of lengths `16` and `8`.

Its area is: `1/2 xx 16 xx 8 = 64`

Explanation:

This is a kite...

graph{((2/3(x+5)-1/3sqrt((x+5)^2)+y-4)^100+(2/3(x+5)-1/3sqrt((x+5)^2)-(y-4))^100-2*4^100) = 0 [-11.13, 8.87, -0.88, 9.12]}

If we add diagonals and enclosing rectangle, then you can see that its area is one half of the area of the rectangle...

graph{((2/3(x+5)-1/3sqrt((x+5)^2)+y-4)^100+(2/3(x+5)-1/3sqrt((x+5)^2)-(y-4))^100-2*4^100)(y-4)(x+5)(((x+1)/2)^100+(y-4)^100-4^100) = 0 [-11.13, 8.87, -0.88, 9.12]}

The enclosing rectangle is `16 xx 8`, so the area of the kite is:

`1/2 xx 16 xx 8 = 64`