Problem Solving Set #3

7. In this diagram, square ABCD has side length 2, with M the midpoint of BC and N the midpoint of CD. The area of the yellow region BMND is. . .

It took me a few tries before I got the answer to this question, but once I realized what to do, it was pretty easy. First you have to find out the area of the triangle ABD. The formula for triangles is side time side divided by 2. So, just plug it in and you get 2 times 2 divided by 2. That gives you... 2! Yeah! So the area of triangle ABD is 2.


Now you have to find the area of angle NMC! Before you do this you have to figure out what sides NC and MC are. By reading the question again you see that N and M are midpoints; meaning that on each side of these points is 1... because 1 plus 1 equals 2! So now you know that MC and NC both equal 1. By knowing this we can plug it in and we get 1 times 1 divided by 2. This equals... 0.5! YAY!


Sadly we have not quite finished the question so we have to rap it all up by actually finding the shaded area. We take triangle ABD and triangle MNC and minus them from the entire square which is 4. This will look like 4 minus (2 + .5) = 1.5. There now you`re done. 1.5. That's all there is to it.


The area of the shaded region of BMND is (D) 1.5


Well actually the answer puts in in 3 over 2 form, but it's the same thing. 3 over 2 is the same as 1.5

Problem Solving Set #2

For this set of questions I will pick number 16 to show. I like this question because, you can use math or just common sense ! Here's the question.

16. On a rectangular table 5 units long and 2 units wide, a ball is rolled from point P at an angle of 45 degrees to PQ and bounces of SR. The ball continues to bounce of the sides at 45 degree angles until it reaches S. How many bounces of the ball are required?

The first thing I did was read the question a few times to make sure I knew what I was supposed to be looking for. Then I looked at the rectangle given and tried to figure out where to start. Then when you realized that each bounce is 45 degrees and it's starts at P I started drawing the path of which the ball would've taken. This is one answer.

Or you can mathematically deduct that each roll between the bounce off another wall will be 2 units, except for the end where there is not enough space. There is only enough room for 5 bounces, no more, no less.

So the answer = (D) 5

P.S. Everything in the picture that is black was given with the question. Everything in Red (or whatever that colour is) is what I drew to help figure it out.