Math Issue (school)

ID:181583
 
Feb 14 2010, 11:18 am (Edited on Feb 14 2010, 11:24 am)
So I am supposed to solve the area of this triangle right (and many others). So, a triangle formula is 1/2 of the base times the height. This triangle is 2 by 2 on graph paper, and has a total of two blocks

Now, every two boxes count as one foot. Which would mean in theory that every box is .5(half) of a foot. So here is what I did:

Shape -- Original -- 1/2 base-- Feet Conversion

Triangle 1 -- 2 by 2 -- 1 by 2 -- .5 by 1



Area Each
.5 foot.


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So after getting the feet conversion I multiply the base times height and get .5 feet. Well the only issue is that there are two boxes inside the triangle in total, which would add up to 2. Then if I changed it into feet, it should equal one foot. What am I doing wrong?
Feb 14 2010, 11:34 am
You're playing fast and loose with your units, which is confusing the issue. You're working with feet, square feet, graph paper units, and square units, but you're using some of them interchangeably. The area for instance is not in feet; it's in square feet.

You do have a conversion of 2 units = 1 foot, which means 4 square units = 1 square foot. But you don't really need square units.

If the triangle is a right triangle with its short sides both equalling 2 units (1 foot), then your formula is:

A = ½ × (1 foot) × (1 foot)
A = ½ × (1 square foot)
A = ½ square foot

Doing this in graph paper units will yield the same result.

A = ½ × (2 units) × (2 units)
A = ½ × (4 square units)
A = 2 square units

Since 1 square foot is equal to 4 square units, you can use that in a unit conversion fraction .

A = 2 square units × (1 square foot / 4 square units)
A = ½ square foot

Lummox JR
Feb 14 2010, 1:38 pm
In response to Lummox JR
Thank you so much Lummox =)