### 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 .

**Possible Answers:**

**Correct answer:**

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 #2 : How To Find If Rectangles Are Similar

Note: Figure NOT drawn to scale.

In the above figure,

.

.

Give the area of .

**Possible Answers:**

Insufficient information is given to determine the area.

**Correct answer:**

Corresponding sidelengths of similar polygons are in proportion, so

, so

We can use the Pythagorean Theorem to find :

The area of is

### 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 .

**Possible Answers:**

**Correct answer:**

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 #4 : 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 ?

**Possible Answers:**

Insufficient information is given to answer the problem.

**Correct answer:**

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 #5 : How To Find If Rectangles Are Similar

Note: figure NOT drawn to scale.

Refer to the above figure.

, , .

Give the area of .

.

**Possible Answers:**

**Correct answer:**

, so the sides are in proportion - that is,

Set

, , and solve for :

has area