### All PSAT Math Resources

## Example Questions

### Example Question #1 : Quadrilaterals

A trapezoid has a base of length 4, another base of length *s*, and a height of length *s*. A square has sides of length *s*. What is the value of *s* such that the area of the trapezoid and the area of the square are equal?

**Possible Answers:**

**Correct answer:**

In general, the formula for the area of a trapezoid is (1/2)(*a* + *b*)(*h*), where *a* and *b* are the lengths of the bases, and *h* is the length of the height. Thus, we can write the area for the trapezoid given in the problem as follows:

area of trapezoid = (1/2)(4 + *s*)(*s*)

Similarly, the area of a square with sides of length *a* is given by *a*^{2}. Thus, the area of the square given in the problem is *s*^{2}.

We now can set the area of the trapezoid equal to the area of the square and solve for *s*.

(1/2)(4 + *s*)(*s*) = *s*^{2}

Multiply both sides by 2 to eliminate the 1/2.

(4 + *s*)(*s*) = 2*s*^{2}

Distribute the *s* on the left.

4*s* + *s*^{2} = 2*s*^{2}

Subtract *s*^{2} from both sides.

4*s* = *s*^{2}

Because *s* must be a positive number, we can divide both sides by *s*.

4 = *s*

This means the value of *s* must be 4.

The answer is 4.

### Example Question #1 : Trapezoids

Note: Figure NOT drawn to scale.

The white region in the above diagram is a trapezoid. What percent of the above rectangle, rounded to the nearest whole percent, is blue?

**Possible Answers:**

**Correct answer:**

The area of the entire rectangle is the product of its length and width, or

.

The area of the white trapezoid is one half the product of its height and the sum of its base lengths, or

Therefore, the blue polygon has area

.

This is

of the rectangle.

Rounded, this is 70%.

### Example Question #2 : How To Find The Area Of A Trapezoid

Refer to the above diagram. .

Give the area of Quadrilateral .

**Possible Answers:**

**Correct answer:**

, since both are right; by the Corresponding Angles Theorem, , and Quadrilateral is a trapezoid.

By the Angle-Angle Similarity Postulate, since

and

(by reflexivity),

,

and since corresponding sides of similar triangles are in proportion,

, the larger base of the trapozoid;

The smaller base is .

, the height of the trapezoid.

The area of the trapezoid is

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