Question

Help with this please it is due tomorrow and I have no clue how to do it.

Answer 1

We are told to calculat the percentage of the flag that is white. To do so, we will proceed to calculate the following

`\frac{\text{Area of the white part}}{Area\text{ of the flag}}`

So, let us consider first the diagram of the flag

The whole flag is a triangle of dimensions 6 x 8 . Recall that the area of a rectangle is

`b\cdot h`

where b is the base of the rectangle and h is the height. IN our case, we have b=8 and h = 6 so the area of the whole flag would be

`8\cdot6=48`

(48 squared inches).

Now, recall that the area of the flag that is white is the same as taking the whole area of the flag and subtracting the area of the flag that is not white. So, we need to calculate the area that is not white.

Note that the area that is not white consists of 4 triangles. One pair of triangles of dimensions 4x3 and one pair of triangles of dimensions 6x2. Recall that the area of a triangle of base b and height h is given by

`(b\cdot h)/(2)`

Let us calculate the area of the triangles on the sides. This are triangles of base 4 and height 3. So the area of one triangle would be

`(4\cdot3)/(2)=(12)/(2)=6`

Since we have 2 triangles, we should multiply this number by 2. So the total area for the triangles on the sides is

`6\cdot2=12`

(12 squared inches).

For the triangles that are on the top and bottom, we have a pair of triangles of base 6 and height 2. So we have that the area of one triangle would be

`(6\cdot2)/(2)=6`

Since we have two triangles, we multiply this number by 2. So we get

`6\cdot2=12`

Now, we add this two number, to calculate the area of the flag that is not white, that is

`12+12=24`

Now, we subtract this number from the total area of the flag, so we would get the area of the flag that is white. That is

`48\text{ -24=24}`

Finally, to calculate the percentage we divide this number by the area of the whole flag. So, the percentage of the flag that is white is

`(24)/(48)=(1)/(2)=0.5`

That is, 50% of the flag is white.