Farmer Bob has four straight pieces of fencing: 1, 2, 3, and 4 yards in length. What is the maximum area he can enclose by connecting the pieces? Assume the land is flat.
what i did was make a isosceles triangle of all the pieces. 4 is the base and 3 is the height, and on the other side, i put the 2 and 1 together to get 3 as well. the formula for area of a triangle is base x height/2, so the space enclosed is 6 yards squared
One way to cover to area is to put 4 on the bottom 3 on one side and the the 2 and 1 on the other. The area is 4.47214 yards. I used an isoceles triangle calculator
i made a triangle, i think, its the one where you put like, 1 plus 2 and 3 on both sides and the base is like, 4, so then ya, i got 6 unit things, i guess yards, and i was thinking of doing an irregular square but i didnt know how, so then i tried making a square with one of the line going sideways, so i found out that the triangle works best... i think...! bye... love u like a fat kid love cake!
I would make an isosceles triangle with a base of 4 yards. Both sides would equal 3 yards in length; one would be the 3 yard piece and the other side would be the 2 and 1 yard pieces put together. Like Iris and Liam I got an area of 6 yards squared. This is because the formula for finding the area of a triangle is base X height/2. The base is 4 yards and the height is 3 yards, (4 X 3=12, 12/2=6.)
I think that you have to make an icocoles triangle since it is impossible to make a Quadrellateral out of 4 pieces of different length. So four yards on the base, 3 yards on one side, and 2 and 1 yard pieces put together on the other side. The total area is 6m2 since the formula is B*H/2= area, and 4(base) times 3(height) = 12, and 12 divided by 2 is 6
Well, I am assuming you need to make a triangle, because I do not think I could calculate the area of the figure if it had four uneven sides. I made several different triangles (e.g. I put the 4 yards and the 3 yards together, then I used 1 and 2 yards as the other sides. I also tried other ones.) Then, I made a triangle using 3 yards, 4 yards, and I put 1 and 2 yards together. It had an area of 6 yards. That is the largest area I could find.
ok so my total area is 6 yards squared. why? becuase i made a triangle, the base is 4 than the length is 3, the short side is the remaining 1+2(3). to get area of a triangle you do Base times Height then divided by 2 so it would be 4times3=12 divided by 2=6,this is the largest number i can find all the others are either smaller of mathematically not a makeable shape.
First, you make an isoceles triangle with sides of 3 yards and a base of 4 yards. The height, h, of this isoceles triangle is given by h squared = (3 squared - 2 squared) yards. The area of the isoceles triangle is 1/2 x base x h = 1/2 x 4 x h = 2 x h squared yards. However, the maximum area you can enclose is by making a quadrilateral with sides of 1 x 2 x 3 x 4 yards and this area will be slightly bigger than the area of the isoceles triangle above.
OK, so this is my answer (6) and here is my explanation. I found this because the length of the isoceles triangle i decided to make is 3x3x4. This in a rectangular shape is 3x4 which is 12. But, the differece between the area of a triangle and a rectangle is that the area of the triangle is divided by 2 while the rectangle is not. In simpler form, while the area of the rectangle is LxW and the area of a triangle is BxH/2. As I was saying, the triangle in a 'rectangular form' would be 4x3 which gives you its area (12.) So, to calculate the triangular form of the figure you would have to divide it by two (12/2.) So, the largest area of enclosing with a fence of these dimentions is 6yards2.
what i did was make a isosceles triangle of all the pieces. 4 is the base and 3 is the height, and on the other side, i put the 2 and 1 together to get 3 as well. the formula for area of a triangle is base x height/2, so the space enclosed is 6 yards squared
ReplyDeleteOne way to cover to area is to put 4 on the bottom 3 on one side and the the 2 and 1 on the other. The area is 4.47214 yards. I used an isoceles triangle calculator
ReplyDeletei made a triangle, i think, its the one where you put like, 1 plus 2 and 3 on both sides and the base is like, 4, so then ya, i got 6 unit things, i guess yards, and i was thinking of doing an irregular square but i didnt know how, so then i tried making a square with one of the line going sideways, so i found out that the triangle works best... i think...! bye... love u like a fat kid love cake!
ReplyDeleteI would make an isosceles triangle with a base of 4 yards. Both sides would equal 3 yards in length; one would be the 3 yard piece and the other side would be the 2 and 1 yard pieces put together. Like Iris and Liam I got an area of 6 yards squared. This is because the formula for finding the area of a triangle is base X height/2. The base is 4 yards and the height is 3 yards, (4 X 3=12, 12/2=6.)
ReplyDeleteI think that you have to make an icocoles triangle since it is impossible to make a Quadrellateral out of 4 pieces of different length. So four yards on the base, 3 yards on one side, and 2 and 1 yard pieces put together on the other side. The total area is 6m2 since the formula is B*H/2= area, and 4(base) times 3(height) = 12, and 12 divided by 2 is 6
ReplyDeleteWell, I am assuming you need to make a triangle, because I do not think I could calculate the area of the figure if it had four uneven sides. I made several different triangles (e.g. I put the 4 yards and the 3 yards together, then I used 1 and 2 yards as the other sides. I also tried other ones.) Then, I made a triangle using 3 yards, 4 yards, and I put 1 and 2 yards together. It had an area of 6 yards. That is the largest area I could find.
ReplyDeleteWell i made an isosceles triangle with 3(1+2) 3(3) and 4(4) and then i did base times height divided by two to get 6 that the bigest i could find
ReplyDeleteok so my total area is 6 yards squared. why? becuase i made a triangle, the base is 4 than the length is 3, the short side is the remaining 1+2(3). to get area of a triangle you do Base times Height then divided by 2 so it would be 4times3=12 divided by 2=6,this is the largest number i can find all the others are either smaller of mathematically not a makeable shape.
ReplyDeleteAdele
First, you make an isoceles triangle with sides of 3 yards and a base of 4 yards. The height, h, of this isoceles triangle is given by h squared = (3 squared - 2 squared) yards. The area of the isoceles triangle is 1/2 x base x h = 1/2 x 4 x h = 2 x h squared yards. However, the maximum area you can enclose is by making a quadrilateral with sides of 1 x 2 x 3 x 4 yards and this area will be slightly bigger than the area of the isoceles triangle above.
ReplyDeleteOK, so this is my answer (6) and here is my explanation. I found this because the length of the isoceles triangle i decided to make is 3x3x4. This in a rectangular shape is 3x4 which is 12. But, the differece between the area of a triangle and a rectangle is that the area of the triangle is divided by 2 while the rectangle is not. In simpler form, while the area of the rectangle is LxW and the area of a triangle is BxH/2. As I was saying, the triangle in a 'rectangular form' would be 4x3 which gives you its area (12.) So, to calculate the triangular form of the figure you would have to divide it by two (12/2.) So, the largest area of enclosing with a fence of these dimentions is 6yards2.
ReplyDeletecut em up, make a (near) circle with circumference of 10 and calculate area.
ReplyDelete