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