Question

how to find the area of a rhombus with vertices: (-1,-1) , (9,4) , (20,6) and (10,1)

Answer 1

first step is to graph it...

Answer 2

i did

Answer 3

but I don't know what to do next

Answer 4

can you draw a rough sketch?

Answer 5

here

Answer 6

can you label the points too?

Answer 7

now use the distance formula to find the distance between (9,4) and (10,1) then you will have two nice easy triangles you can easily use A=1/2bh to solve for. then multiply by 2 to find the whole shape's area

Answer 8

Do you know cross product?

Answer 9

yea

Answer 10

It is easier with cross product. You have to add 0 for z for each point. So you will be in 3D.
\[
Area=\frac 1 2\left| AB \times AC \right|

\]

Answer 11

i thought it was the area is just the magnitude of the cross product, not half of it.... but i took vector calculus some yrs ago...

Answer 12

this is for pre-calculus

Answer 13

You can take
A={-1, -1, 0}
B={9, 4, 0}
C={20, 6, 0}

Answer 14

You are right. I was think about the triangle.

Answer 15

indeed.

Answer 16

\[
Area=\left| AB \times AC \right|
\]

Answer 17

I am not saying that one has to do it this way.

Answer 18

how would you plug the numbers in?

Answer 19

For precalculus, use the distance formula.

Answer 20

I used it to split the rhombus in half to make 2 triangles

Answer 21

Alternatively, you can use the formula

A = (pq)/2

where p and q are the lengths of the diagonals. So you'll need to use the distance formula to find the lengths of the diagonals.