An 84 meter length of fencing is attached to the side of a barn in order to fence in a rectangular area, as shown in the figure above. If the length of the side of the fence running perpendicular to the barn is half the length of the side of the fence that is running parallel to the barn, what is the area of the fenced off land?

Will you please answer question # 27, Test 3, section 4. Is it possible to use real numbers in your example? Thanks!

Hi Mike,

question on Math Quiz 4 #9: I get the answer and the proposed solution (area of large triangle minus area of small triangle). But my daughter worked the problem differently and I think what she did was correct, but she got a slightly different answer and I can’t figure out exactly why.

Her solution: she used Pythag Theorem to get the hypot of small triangle: so 4^2 + 1^2 = c^2…. so c=Sqrt(17). This is base of large triangle. So A= 1/2 bXh, or 1/2 (sqrt 17)(8), she got 16.492.

If points (6,0), (0,0), (0,2), and (a,2) are consecutive vertices of a trapezoid of area 7.5, what is the value of a?

A) 1.5

B) 2

C) 2.5

D) 5

E) 9

Yesterday I went to a museum and waited in line for a very long time for my turn to spend 5 minutes staring at a piece of art that completely mystified me. I guess it’s good art if I’m still thinking about it a day later, even if the thoughts I’m having mostly revolve around (more…)

Since you guys tore up my last challenge question so quickly, I figured I’d make this one a tiny bit harder. Let’s see if I can’t stump you for more than 8 minutes. First correct response in the comments gets a free Math Guide. Usual contest rules apply. Ready? Here we go! In the figure (more…)

I’m heading out this morning to go camping for the weekend (Woohoo! Bug bites!) and I won’t have any way to access the Internet reliably, so if you enter this contest please be patient. I probably won’t be able to declare a winner or post a solution until Monday evening. I’m told the place we’ll (more…)

In honor of Father’s Day, this weekend challenge is inspired by my dad’s hobby business. He sells wooden flags, like the one above, on Etsy. Basically, he finds discarded pallets (this is a pallet), chops ’em up into pieces of the size he needs, and mounts them. As usual, these challenge questions are not really (more…)

If you’ve ever sat down and taken a practice (or real) SAT, you’ve come across shaded region questions. They’re among the most iconic question types on the test, so much so that you may find that the memory of them remains with you long after your SAT taking days have passed. True story: I had (more…)

Before we get into triangles, we need to take a very quick look at the ingredients of a triangle: line segments and angles. Please tell me you already know this stuff: We good? Cool. Prove it: In the figure above, AE, BS, CG, DS, and FS intersect at point S. Which of the following (more…)

This is a little harder than a typical SAT question, and obviously formatted with a bit more flair and color than the College Board would use, but it deals with the same concepts you’ll need to master to kick the SAT where it hurts most, so have a go at it: I looked out my (more…)

In the figure above, AB is the diameter of the circle, and AC = BC. What is the area of the shaded region? (A) 4π – 2 (B) 2π – 1 (C) π (D) π – 1 (E) π – 2 Answer and explanation after the jump… As is usually the case with shaded region problems, the easiest way (and in this (more…)