Question

What is the area of the quadrilateral ABCD with vertices A(0,3), B(3,3), C(5,2), D(5,0)?

Answer 1

I've found out that the distance between A and B is 3, between B and C is sqrt(5), between C and D is 2, and between A and D is sqrt(34), but I don't know how to find the area when I don't have the height, but have the sides.

Answer 2

well the quadrilateral is a trapezoid, when you plot the points..

you need to find the lengths of the parallel sides BC and AD

then you need the perpendicular height.

you need to find the equation of the line AD

then use the equation for perpendicular distance from a line to a point

\[d = \frac{\left| Ax_{1} + By_{1} + C \right|}{\sqrt{A^2 + B^2}}\]

choose either point B or C for (x1, y1)

but you do need to find the equation of the line segment AD. IT should be easy if you look at the graph.

Hope it helps

Answer 3

once you have the lengths of BC = a and AD = b as well as the perpendicular height = h, you can find the area.

\[A = \frac{h}{2}(a + b)\]