# Finding areas of rectangles.

1. Apr 29, 2016

### Kirito123

1. The problem statement, all variables and given/known data

2. Relevant equations

A= l x w (area for a rectangle.

3. The attempt at a solution

I will have to find the area of 1 halve of the roof, since there parallel I only have to find one side. So I know the height is 2 and I also know that the base of the rectangle is 8. I tried to find out but had no luck.

So my only problem is how do I find the other side of the rectangle?

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2. Apr 29, 2016

### ProfuselyQuarky

The height of the yellow rectangle is not, in fact, 2.

3. Apr 29, 2016

### Kirito123

Its not???

4. Apr 29, 2016

### ProfuselyQuarky

Nope. That is the height of the triangle. There are completely different lengths. How do you think we can find the height of the rectangle?

5. Apr 29, 2016

### Kirito123

I don't know but my guess is i have to find all the lengths of the triangle then i can answer the question.

6. Apr 29, 2016

### ProfuselyQuarky

The height of the rectangle is the side length of the triangle. You already know the height and base measurements for the triangle, which is all the information you need. Do you know how to find the side length of a triangle?

7. Apr 29, 2016

### Nidum

Draw end view to scale or use Pythagoras' Theorem

8. Apr 29, 2016

### ProfuselyQuarky

This is extremely inefficient, is it not?

The Pythagorean Theorem will work, but the OP was supposed to figure that out.

9. Apr 29, 2016

### Kirito123

so i would use the formula a2 + b2= c2.

a2 + b2 = c2

m2 + m2 = 5m2 (Note: i am using m to represent the unknown lengths of the triangle)

2m2 = 25

2m2 / 2 = 25 / 2

m2 = 12.5

m = 3.5

the length of the unknown sides is approximately 2.5 m

Correct?

10. Apr 29, 2016

### ProfuselyQuarky

This is wrong, though. In $a^2+b^2=c^2$, do you know what the c stands for?

11. Apr 29, 2016

### ProfuselyQuarky

And for the Pythagorean Theorem to work, you need a right triangle.

12. Apr 29, 2016

### Kirito123

c is the hypotenuse (the side opposite the 90° angle).

O do you mean that the triangle isn't a right angle?

13. Apr 29, 2016

### Kirito123

Ok so thats why it won't work.

14. Apr 29, 2016

### ProfuselyQuarky

It CAN work. How would you "make" a right triangle for the Pythagorean Theorem to work? What values would you use?

15. Apr 29, 2016

### ProfuselyQuarky

Break the triangle apart. You can still use the Pythagorean Theorem!

16. Apr 29, 2016

### Kirito123

:O omg you just saved me 3 hours of searching... the fact that on the table above, i did that but didn't even notice.... Ok ill answer it and repost to check if its right.

17. Apr 29, 2016

### ogg

Please note that while the drawing seems to show that the roof is composed of two pieces of equal size, one of which is in yellow, there seems to be an unfounded assumption that the roof is composed of two identical pieces (one slanting down to the left, one slanting down to the right). All you know from the given information is that the length of the two triangles on one end (which share the red "height" line) sum to 5; the assumption that each is 2.5 is not justified. Another way of saying this is that the location of where the roof peak is (what distance from the front) is unspecified. I would solve this poorly specified problem by assuming the two pieces were of equal size and then for extra credit assume that one piece has 0 length (that is, the peak happens at the very back (making the one triangle on each end a right triangle.))

18. Apr 29, 2016

### Kirito123

Ok so i got the answer for 1 halve of the triangle. I would divide 5 into 2 parts, so its become 2.5. I also have the height 2 for the triangle. Now i can use the Pythagorean Theorem to solve for the hypotenuse. a2 + b2 = c2.

2.5 x 2.5 = 6.25
2 x 2 = 4

6.25 + 4 = 10.25

= 3.2

so the length of side of the rectangle would be approximately 3.2m.

19. Apr 29, 2016

### Nidum

That's it .

20. Apr 29, 2016

### Kirito123

ok now i can find the area by my self THX ALOT guys.