mathcounts

sri340 · Poincare Conjecture Offline Joined: 09 Jan 2008 Posts: 218

Triangle ABC has its vertices at A(0,4), B(0,9) and C(6,9). What is the area of the triangle, in square units?

**Posted:** Fri Nov 06, 2009 3:11 am

gauss1181

If you draw out the triangle on the x-y coordinate plane, you'll see it has a base of 5 and a height of 9. So the area is just $\frac{1}{2}(5)(9)=\boxed{22.5}$ square units.

**Posted:** Fri Nov 06, 2009 7:24 am

_________________
My Olympiad Compilation! (plus some bits of randomness too)
Latest Problems Typed: 1979 ISL number theory problem

monkeygirl13

Here is a much faster way to do the problem.
Solution

**Posted:** Fri Nov 06, 2009 3:28 pm

_________________
"For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. John 3:16 NIV Mr. Green

Check out This Blog

randomguy64

I agree with monkeygirl.

**Posted:** Fri Nov 06, 2009 5:05 pm

Stank

Monkeygirl - Your solution works just fine; however, it's important to graph it (or at least look at the slopes of the lines). For all you know, they could have made it some irregular triangle and you would have needed to use Herron's Formula, Shoelace Formula, etc.

**Posted:** Fri Nov 06, 2009 7:00 pm

_________________
Check out or post on my computer generated Math/Science image gallery! http://www.artofproblemsolving.com/Forum/album.php?t=306615

"Your solution may be faster, but the quadratic formula's for squares!" -SP

randomguy64

You realize that (0, 9) and (0, 4) share the same x value, and (6, 9) and (0. 9) share the same y-value, making the triangle right and half a rectangle that is "parallel" to the axes...

**Posted:** Fri Nov 06, 2009 7:44 pm

mathkid95

Well, You could plot the points out and use the distance formula for the base and height and multiply that by $\frac {1}{2}$

So, it is $\sqrt {(x_2 - x_1)^{2} + (y_1 - y_ 2)^{2}}$

Plug in what you know and you get the distances between the base: BC and the height: AB to get

$\frac {1}{2}(5)(6) = 15$

The area is $15$ square units

**Posted:** Sat Nov 07, 2009 8:19 am

_________________
Rotfl

$\text{M^{A}T H_{R^{U_{L_{E{S}}}}}}$