All PSAT Math Resources
Example Questions
Example Question #1 : How To Find If Rectangles Are Similar
Note: Figure NOT drawn to scale.
In the above figure,
.
.
Give the perimeter of .
We can use the Pythagorean Theorem to find :
The similarity ratio of  to  isÂ
so  multiplied by the length of a side of  is the length of the corresponding side of . We can subsequently multiply the perimeter of the former by  to get that of the latter:
Example Question #2 : How To Find If Rectangles Are Similar
Note: Figure NOT drawn to scale.
In the above figure,
.
.
Give the area of .
Insufficient information is given to determine the area.
Corresponding sidelengths of similar polygons are in proportion, so
, so
We can use the Pythagorean Theorem to find :
The area of  isÂ
Â
Example Question #3 : How To Find If Rectangles Are Similar
Note: Figure NOT drawn to scale.
In the above figure,
.
.
Give the area of Polygon .
Polygon  can be seen as a composite of right  and , so we calculate the individual areas and add them.
The area of  is half the product of legs  and :
Â
Now we find the area of . We can do this by first finding  using the Pythagorean Theorem:
The similarity of  to  implies
so
The area of  is the product of  and :
Â
Now add:Â , the correct response.
Example Question #4 : How To Find If Rectangles Are Similar
Note: Figure NOT drawn to scale.
Refer to the above figure.Â
 and .
What percent of  has been shaded brown ?
Insufficient information is given to answer the problem.
 and , so the similarity ratio of  to  is 10 to 7. The ratio of the areas is the square of this, orÂ
orÂ
Therefore,  comprises  of , and the remainder of the rectangle - the brown region - is 51% of .
Example Question #5 : How To Find If Rectangles Are Similar
Note: figure NOT drawn to scale.
Refer to the above figure.Â
, , .
Give the area of .
.
, so the sides are in proportion - that is,
SetÂ
, ,  and solve for :
 has areaÂ