Question 14. Tony the gardener planted tulips and daisies in a square flowerbed with a side length of 12 meters, arranged as shown. What is the total area of the regions in which he planted daisies? We can take a look at the diagram and mark it out with the 4 meters that we know. Since the side length is 12, we can subtract 4 and know that this segment will be equal to 8 meters. We can also draw a diagonal through this entire square, and then erase half of it, so we have a triangle. Next, since this cross section is the midpoint, we know that we have to have 6 meters here, that is half of 12 meters, and this little segment will also be 2 meters. Next, since we are trying to find the area of the regions with daisies, we want to find out the area of one of these triangles. And to find the area of a triangle, we do base times height divided by 2. So we will be doing 4 times 6 divided by 2, and this gives us a total of 12. Now we have to remember that there are two such sections on this triangle, so we have to multiply this by 2. But we also have to remember that we erased half of this square, so we will in fact actually be multiplying it by 2 again, or by 4 in total. So when we do 12 times 4, we will get our answer, which will be a, 48 meters squared.

gardener

daisies

triangles

flowerbed

area