# ISEE Lower Level Quantitative : Plane Geometry

## Example Questions

### Example Question #1 : Quadrilaterals

What is the area of a trapezoid if its height is 1, its long base is 4, and its short base is 2?

Possible Answers:

Correct answer:

Explanation:

The area of a trapezoid is given by the formula .

We know that the height is 1, the long base is 4, and the short base is 2.

### Example Question #1 : Plane Geometry

Which formula would you use to find the area of a trapezoid?

Possible Answers:

Correct answer:

Explanation:

The find the area of a trapezoid, use:

### Example Question #2 : Plane Geometry

The above diagram shows a trapezoidal home within a rectangular yard. What is the area of the yard?

Possible Answers:

Correct answer:

Explanation:

The area of the yard is the area of the small trapezoid subtracted from that of the large rectangle. The area of a rectangle is the product of its length and its height, so the large rectangle has area

square meters.

The area of a trapezoid is half the product of its height and the sum of its two parallel sides (bases), so the small trapezoid has area

square meters.

The area of the yard is the difference of the two:

square meters.

### Example Question #4 : Quadrilaterals

Note: Figure NOT drawn to scale.

Mr. Smith owns the triangular piece of land seen in the above diagram. He sells the trapezoidal parcel shown at bottom right to his brother. What is the area of the land he retains?

Possible Answers:

Correct answer:

Explanation:

The area of a triangle is half the product of its base and its height, so Mr. Smith's parcel originally had area

square feet.

The area of a trapezoid is the half product of its height and the sum of its two parallel sides (bases), so the portion Mr. Smith sold to his brother has area

square feet.

Therefore, Mr. Smith retains a parcel of area

square feet.

### Example Question #3 : Plane Geometry

What is the area of the above trapezoid?

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a trapezoid is

In other words, find the average of the bases and multiply by the height. Substituting in the values of the bases for the given trapezoid,  and , you get:

### Example Question #6 : Quadrilaterals

What is the area of the above trapezoid?

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a trapezoid is

In other words, find the average of the bases and multiply by the height. Substituting the values of the bases of the given trapezoid,  and , into the equation, you get:

The area of the trapezoid is thus .

### Example Question #7 : Quadrilaterals

Find the perimeter of the following trapezoid.

Possible Answers:

Correct answer:

Explanation:

In order to find the perimeter of the trapezoid, we have to add up all the outer sides:

### Example Question #8 : Quadrilaterals

Find the perimeter of the following trapezoid.

Possible Answers:

Correct answer:

Explanation:

In order to find the perimeter we must add up all the outer sides of the trapezoid.

### Example Question #4 : Plane Geometry

Daria found the perimeter of the below trapezoid to be 29 inches.

What is the length of the missing side?

Possible Answers:

Correct answer:

Explanation:

To find the perimeter of a trapezoid, add up the lengths of its four sides. In the given trapezoid,

To find the missing side, combine like terms and solve for :

The missing side of the trapezoid is  long.

### Example Question #10 : Quadrilaterals

What is the perimeter of the above trapezoid?

Possible Answers:

Correct answer:

Explanation:

To find the perimeter of a trapezoid, add up the lengths of the four sides. In the given trapezoid,