##### Like what you saw?

##### Create FREE Account and:

- Watch all FREE content in 21 subjects(388 videos for 23 hours)
- FREE advice on how to get better grades at school from an expert
- Attend and watch FREE live webinar on useful topics

# Area With Determinants - Problem 3

###### Norm Prokup

###### Norm Prokup

**Cornell University**

PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

I have another problem here. I have 4 points R, O, F and L, and I want to find the area of the quadrilateral they form. It turns out that this quadrilateral is not a parallelogram. So we’re going to have to get creative in our method for finding the area. Let me show you the plotted points. Here’s point R, O, F, and L.

My strategy here, is going to be to divide this quadrilateral into two triangles. We know how to find the area of triangles. I’m going to find the area of each of these triangles; ROL and RLF, and those will add up to the area of quadrilateral ROFL.

Area of ROFL equals the area of triangle ROF plus the area of triangle RLF, those two triangles. Now let’s remember that, the area of a triangle is going to be ½ the absolute value of a determinant formed by two vectors, that make up two sides, that share an initial point of the triangle. Let’s try RO and RF.

Vector RO and vector RF. I need to come up with components for these guys. RO goes from point R to point O, and so it’s going to be 0 minus 2, -2, 0 minus 6, -6. And RF is from R to point F, 7 minus 2, 5, 1 minus 6, -5. So my determinant is going to be <-2,-6> <5,-5>.

Plus I need to find the area of RLF and so I’m going to need two more vectors. RL, I already have RF. So I can use this very same RF, <5, -5>. RL is going to be from point R to point L. so 7 minus 2, 5, 4 minus 6, -2. And so here I’m going to have ½ the absolute value of the determinant, 5 -2, 5 -5. This is going to be ½ the absolute value of 10 minus -30, 10 plus 30, 40. That’s going to 20 plus ½ the absolute value of -25 minus -10. -25 plus 10, -15. Absolute value of -15 is 15, times ½ is 7.5. So the total area is 27.5.

Now let’s go back to our picture. What we found was triangle ROF has an area of 20 and RLF has an area of 7.5, for a total area of 27.5.

Please enter your name.

Are you sure you want to delete this comment?

###### Norm Prokup

PhD. in Mathematics, University of Rhode Island

B.S. in Mechanical Engineering, Cornell University

He uses really creative examples for explaining tough concepts and illustrates them perfectly on the whiteboard. It's impossible to get lost during his lessons.

Thiswas EXCELLENT! I am a math teacher and have been looking for an easy/logical way to explain the lateral area of a cone to my students and this was incredibly helpful, thank you very much!”

I just learned more In 3 minutes of polygons here than I do in 3 weeks in my math class”

Hahaha, his examples are the same problems of my math HW!”

###### Get Peer Support on User Forum

Peer helping is a great way to learn. Join your peers to ask & answer questions and share ideas.

##### Concept (1)

##### Sample Problems (3)

Need help with a problem?

Watch expert teachers solve similar problems.

## Comments (0)

Please Sign in or Sign up to add your comment.

## ·

Delete