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 is
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 #3 : Rectangles
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 is
Example Question #5 : Rectangles
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 :
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 :
Now add: , the correct response.
Example Question #1 : How To Find If Rectangles Are Similar
Note: Figure NOT drawn to scale.
Refer to the above figure.
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, or
or
Therefore, comprises of , and the remainder of the rectangle - the brown region - is 51% of .
Example Question #311 : Plane Geometry
Note: figure NOT drawn to scale.
Refer to the above figure.
, , .
Give the area of .
.
, so the sides are in proportion - that is,
Set
, , and solve for :
has area