Thread: Find Area of Quadrilateral

Find area of quadrilateral given A(-4,-2), B(0,5), C(9,3) and D(7,-4).

Since I do not know which quadrilateral it is, I decided to graph the points given on the xy-plane.

I determined it is a parallelogram or so I think.

I found the base to be 11 and height to be 8.

So, A = bh, which is A = 11*8 or 88 but I am wrong according to the math book.

Who is right and why?

Thank you

Here's an idea.

Split it up into 4 triangles and a rectangle and add them all up together, like this:

First triangle: (-4, -2), (0, -2), (0, 5)

2nd tri: (0, 5), (0, 3), (9, 3)

3rd tri: (9, 3), (7, 3), (7, -3)

4th tri: (7, -4), (7, -2), (-4, -2)

Then the rectangle in the middle is (0, -2), (0, 3), (7, 3), (7, -2).

Drawing a picture again should help. It should be easy to calculate this.

Note that you have 2 pairs of triangles which are the same size, which should make the calculation even easier.

Originally Posted by Matt Westwood

Here's an idea.

Split it up into 4 triangles and a rectangle and add them all up together, like this:

First triangle: (-4, -2), (0, -2), (0, 5)

2nd tri: (0, 5), (0, 3), (9, 3)

3rd tri: (9, 3), (7, 3), (7, -3)

4th tri: (7, -4), (7, -2), (-4, -2)

Then the rectangle in the middle is (0, -2), (0, 3), (7, 3), (7, -2).

Drawing a picture again should help. It should be easy to calculate this.

Note that you have 2 pairs of triangles which are the same size, which should make the calculation even easier.

It is easy now but how did you determine those extra points?

I drew it. Draw it yourself and it should be easy to work out how to do it.

Originally Posted by Matt Westwood

I drew it. Draw it yourself and it should be easy to work out how to do it.

It's a rectangle not a parallelogram. I will use graphing paper next time.