Composite shapes area

[A138]

The area I have decided to portion off is created by combining two shapes: a rectangle and an equilateral triangle, with the equilateral triangle directly on top of the rectangle. I have 750 meters of fencing to use (this is the perimeter), and I know the length of the rectangular area needs to be 1.5 times the width. If the base of the triangle is the exact same in measure to the length of the rectangle, what is the area of my shape?

 

[Steven G]

Hi.
This is a math help forum where we help students arrive at the correct answer. This means that you need to be actively involved in finding your solution. Did you read the guidelines for this forum? You really should.

Please draw and post a picture, label as much as you can and try to find the area. If your work is not correct then we will show you where your mistake is.

 

[A138]

I’ve had this since Wednesday. I’ve figured out every other problem except this one. I’ve read it over and over and over and I honestly don’t even know where to start which is why I posted it. Thanks...

 

[A138]

I know that perimeter is distance around an object. I also have the formula for the area.

 

[Steven G]

A couple of comments on your diagram in red. You clearly stated that A_T = A₁ + A₂. Then after finding A₁ and A₂ you MULTIPLIED them and called the result A_T. Why would you do that?

Can you explain why you think that A₂ = (1/2)a*b??

Can you also label all the sides you know, using a and b and possibly something else?

 

[A138]

Those notes were copied directly from the board.

 

[Steven G]

Please draw your own picture and label what you can. We need to make some progress.

 

[Dr.Peterson]

The area I have decided to portion off is created by combining two shapes: a rectangle and an equilateral triangle, with the equilateral triangle directly on top of the rectangle. I have 750 meters of fencing to use (this is the perimeter), and I know the length of the rectangular area needs to be 1.5 times the width. If the base of the triangle is the exact same in measure to the length of the rectangle, what is the area of my shape?

Let's give you a start.

Suppose that the width is x. Write an expression for what the length. Then think about which of a and b is called length, and which is called width.

Then, can you label the length of each of the 5 sides of the combined figure, and write an expression for the perimeter? You can use that to solve for the value of x.

Save your thoughts about area until you've done this much.

 

[A138]

Okay. Is my picture labeled correctly. I truly have no idea what I’m doing. I’m not understanding the concept.

 

[Dr.Peterson]

Okay. Is my picture labeled correctly. I truly have no idea what I’m doing. I’m not understanding the concept.

That's fine, except that you should know what c is. What does equilateral mean?

Now, it will be helpful if you tell us what particular concept you don't understand, and what you are able to do. Do you understand the idea of using a variable x like I suggested? Can you write the expressions I asked you to write?

 

[A138]

Equilateral means all of the angles are the same (they're all 60 degrees), I know that. Does that mean that all the sides of the triangle are 60 as well?????????????

perimeter for a rectangle is 2Lx2W
perimeter for a triangle is A+B+C; side 1 + side 2 + side 3

The only information given is that it all equals 750. I feel like I'm just guessing.

 

[A138]

So this is my equation. How do I begin to solve it? It also says that the length is 1.5 the width, right?

 

[A138]

Or since it's only the outside, would it be 2L+W+2S=750?

 

[Dr.Peterson]

First, did you miss the fact that they tell you the side of the triangle is equal to the LENGTH of the rectangle, not the width? You need to swap the labels L and W.

Second, do you see that you don't need S at all, because it is the same as the actual L?

Third, do you see that you are told that L = 1.5W?

Putting this all together, you can write an equation involving only W.

 

[A138]

Thank you. I watched a YouTube video last night on how to find area with only the perimeter being given and it was explained to me better. The only thing I couldn’t find was a composite shape one like I have. I realized that my length and width were switched and I fixed it. I still don’t think my equation is right.

 

[Dr.Peterson]

The picture is good now.

The equation is not, because 750 is the perimeter, which is found by adding, not multiplying! (And the way you solved would be wrong, probably because you haven't learned how yet ...)

The equation should use the sum of the five sides: 2x + 3(1.5x) = 750.

Solve that for x, and then give some thought to the area of each part. You'll have to use a formula for the area of a triangle, for which you'll need to work out the height, possibly by the Pythagorean theorem. Or you may have a special formula for an equilateral triangle.

Just show what you can do, and maybe tell us a little of what you have learned about areas if you aren't sure what to use.

 

[A138]

I want to make sure this is correct before I move on.

 

[A138]

I forgot to add that I know that the bottom of the triangle is 173.07 as well.

 

[Dr.Peterson]

Great!

Now it's time to think about area.

What is the area of the rectangle?

What do you know about finding the area of the triangle?

 

[A138]

I think I got it. Can you please tell me if I’m correct?