Find x, y, ratios of perimeter and area of two similar polygons

[TinaJena]

This problem is becoming to difficult for my daughter and I to understand and we have tried looking up different ways to solve it to no avail. we was able to find the valuesof x and y, and the ratios, as well as the parameter but we can not figure out how to solve the area. The following image is the problem along with the work that we have done so far. any help would be appreciated.

Thanks in advance,

Tina

 

[Dr.Peterson]

This problem is becoming to difficult for my daughter and I to understand and we have tried looking up different ways to solve it to no avail. we was able to find the values of x and y, and the ratios, as well as the parameter but we can not figure out how to solve the area. The following image is the problem along with the work that we have done so far. any help would be appreciated.

Thanks in advance,

Tina

There actually isn't enough information to calculate the actual areas; the sides could be at various angles that you don't know. (Nothing is parallel, so you can't use the formula for a trapezoid.)

But there is an important fact that you need to know about the ratios of areas of similar figures. If you have not seen it, you could guess it by comparing the areas of, say, two squares with different sizes. The ratio of areas is the square of the ratio of sides. Does that sound familiar?

 

[Steven G]

This problem is becoming to difficult for my daughter and I to understand and we have tried looking up different ways to solve it to no avail. we was able to find the valuesof x and y, and the ratios, as well as the parameter but we can not figure out how to solve the area. The following image is the problem along with the work that we have done so far. any help would be appreciated.

Thanks in advance,

Tina

As Dr Peterson said correctly you can not calculate the area but fortunately you were NOT asked to. You were just asked for the ratio of the two areas.

Please note that the base is a straight line that measure 6. Now the two line at the top (the ones labeled with 3) have a total measure of 6 units as well BUT the two lines do not make a straight line. This means that the two lines marked x must be getting closer at the top then at the bottom. So as was already pointed out no lines are parallel.

Now back to the problem (kind of). If you have a 2x3 rectangle, then the area is 6 square units. If you make a 2nd rectangle by multiplying each side by of the original rectangle by 5, the two rectangles will be similar. The dimensions will now be 10x15 and the area will be 150 square units. Please note that 150/6 = 25 =5². This is true for the area of similar two-dimensions figures, that is if the area of one figure is a and the other is scaled by b, then the new figure will have an area of a*b². This should help you get the ratio of the areas for your daughter's problem.