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!

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