Year 12s: what will be the first way you research your future options? >>

Vectors question - area of quadrilateral

I have a question that I cant seem to find the answer to, im wondering if ayone can spot where im going wrong.

Given points A(1,0,10) B(7,4,0) C(-3,14,0) D(-9,4,16) which are coplanar, calculate the area of the quadrilateral ABCD

The way ive done it is finding AB and AC then using the cross product rule (matrix) to multiply these two together I get my answer as 89 units. But the answer im given on my sheet is 199.

(edited 11 years ago)

Reply 1

WhiteGroupMaths

You have yet to consider point D. Peace.

Reply 2

username931278

I assumed it to be a parallelogram.

Reply 3

WhiteGroupMaths

You can't do that, the quadrilateral doesn't necessarily have to be a parallelogram. Peace.

(edited 11 years ago)

Reply 4

username931278

so what do I do. Find vector CD and then use a 3x3 matrix?

Reply 5

steve2005

Original post by Diggedy

I have a question that I cant seem to find the answer to, im wondering if ayone can spot where im going wrong.

Given points A(1,0,10) B(7,4,0) C(-3,14,0) D(-94,16) which are coplanar, calculate the area of the quadrilateral ABCD

The way ive done it is finding AB and AC then using the cross product rule (matrix) to multiply these two together I get my answer as 89 units. But the answer im given on my sheet is 199.

A, B and C each have three components. So why have you only got two components for D ?

typo! edited

Original post by Diggedy

typo! edited

Split your quadrilateral into two triangles, and work out the area of each. Quick sketch projecting onto the z=0 plane would be useful just to confirm the shape is convex.