## Friday, June 22, 2012

### Problem of the Week Day 5: Week of 6/18/12 - 6/22/12

It is the last day of June’s problem of the week! Remember to email me your answers once you figured them out at Ethan@EthanMath.com. Good luck!
Easy: I like to finish off the week with some geometry. Today, we will use a rectangle.
This rectangle has an area of t and a width of n^2. Try to determine its length.
l =
To do this, you will need the rectangle’s area formula, which is:
A = lw
Say you had an area of 4 and a width of 2. You would do:
4 = l(2)
4 = 2l
4 ÷ 2 = 2l ÷ 2
2 = l
Do the same thing for this problem.
Hard: Before we begin this problem, there is a small calculation I would like you to do.
√(n - 1) = d
d =
Now, we will do some geometry. Take this trapezoid:

What is the area, which we will call z. Round to the nearest hundredth.
z =
To do this, you need to use this formula:
h(b1 + b2)/2
For example, say the top side was 3 cm, the bottom was 4 cm, and the height was 6 cm. You would do:
6(3 + 4)/2
6(7)/2
42/2
21
The area would be 21 sq. cm. Good luck!