Gifted Issues Discussion homepage Forums General Discussion Geometry / game show question

Ok, I'm scratching my head over this one. We were just watching "Are you smarter than a 5th grader" and I can't imagine that they didn't get challenged on this question.

The sides of a triangle are 5, 5, and 6. What is the area?

Now the guy thought it over and went with the cheat to use the kid's answer, which was wrong. When he had answered the question, then they put a picture up on the board showing the triangle with sides of 5, 5, and 6, and a dotted line showing the height to be 4. My brain was fried trying to figure out how they got the 4. After considerable internet searching, I have concluded (tell me if this is wrong) that the "Heron's Formula" that gives the height of 4 from the three side measurements is high school algebra. If they had shown the height as part of the question, that is elementary math (it was a 4th grade question). Am I crazy here?

Hmmm...I recognized right away that an altitude would bisect the original triangle into two Pythagorean triples (3-4-5 right triangles, in this case), but I don't know for sure when they first covered those in my school.

Orient the triangle so that the base is 6.

You cut the triangle in half, leaving you with a pair of right triangles. The base of each rt triangle is 3, and the hypotenuse is 5.

Now just apply that really old guy's theorem: a^2 + b^2 = c^2

You back into the height by taking (c)5^2 less (b)3^2 (25-9), which is 16. The sqrt of 16 is 4. That's your height.
(4^2)+(3^2)=5^2

Area=1/2bh
= .5 * 6 * 4
= 12sq whatevers

My son's school hit that in 5th here in CA.

My daughter didn't have Pythagorean theorem until pre-algebra (which would not be 5th grade). Also in CA.

Ok, I can see that now, and make it work, although I forget how to determine which is A and B and C so as to get the formula in the right order. DS8 is almost done with 7th grade math in ALEKS and says he has a topic on that but hasn't done it yet, and it hasn't shown up in anything up to that.

The hypotenuse ("C") is the side opposite the right angle. A and B are the sides which meet to form the right angle. I always remembered it by saying when you stand in the "right" place and look out, the hypotenuse is the one you "C".

Ahh, ok. It's been far too long! I have to go into the explanations whenever DS8 has a question on ALEKS, to see what they have to say about what to do and how it's done. So far, it's generally coming back long enough for me to help him to understand, but he's getting ahead of my antique, well-worn brain. I need to start on those algebra books again before he gets seriously into it, so I can stay ahead!

I hate my memory. I've had algebra three times in my life, and here I'm going to have to start it for the fourth! It just goes right back out again as soon as I'm done.

Was that here, or somewhere else, that I recently read the explanation that a girl gave, saying that she pours all the information into a funnel, holding the bottom shut with her finger, and when it's test time she turns loose and funnels it all out onto the test paper?