# ISEE Middle Level Math : Trapezoids

## Example Questions

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### Example Question #1 : How To Find The Area Of A Trapezoid

What is the area of the above trapezoid?

Explanation:

To find the area of a trapezoid, multiply one half (or 0.5, since we are working with decimals) by the sum of the lengths of its bases (the parallel sides) by its height (the perpendicular distance between the bases). This quantity is

### Example Question #211 : Geometry

Find the area of the trapezoid:

Explanation:

The area of a trapezoid can be determined using the equation .

### Example Question #212 : Geometry

What is the area of the trapezoid?

Explanation:

To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.

### Example Question #213 : Geometry

The above diagram depicts a rectangle  with isosceles triangle . If  is the midpoint of , and the area of the orange region is , then what is the length of one leg of  ?

Explanation:

The length of a leg of  is equal to the height of the orange region, which is a trapezoid. Call this length/height .

Since the triangle is isosceles, then , and since  is the midpoint of , . Also, since opposite sides of a rectangle are congruent,

Therefore, the orange region is a trapezoid with bases  and  and height . Its area is 72, so we can set up and solve this equation using the area formula for a trapezoid:

This is the length of one leg of the triangle.

### Example Question #214 : Geometry

A trapezoid has a height of  inches and bases measuring  inches and  inches. What is its area?

Explanation:

Use the following formula, with :

### Example Question #1 : How To Find The Area Of A Trapezoid

Find the area of a trapezoid with bases equal to 7 and 9 and height is 2.

Explanation:

To solve, simply use the formula for the area of a trapezoid.

Thus,

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

Find the area of a trapezoid with bases of 10 centimeters and 8 centimeters, and a height of 4 centimeters.

Explanation:

The formula for area of a trapezoid is:

where

therefore the area equation becomes,

### Example Question #3 : How To Find The Area Of A Trapezoid

You recently bought a new bookshelf with a base in  the shape of an isosceles trapezoid. If the small base is 2 feet, the large base is 3 feet, and the depth is 8 inches, what is the area of the base of your new bookshelf?

Cannot be determined from the information provided.

Explanation:

You recently bought a new bookshelf with a base in  the shape of an isosceles trapezoid. If the small base is 2 feet, the large base is 3 feet, and the depth is 8 inches, what is the area of the base of your new bookshelf?

To find the area of a trapezoid, we need to use the following formula:

Where a and b are the lengths of the bases, and h is the perpendicular distance from one base to another.

We are given a and b, and then h will be the same as our depth. The tricky part is realizing that our depth is in inches, while our base lengths are in feet. We need to convert 8 inches to feet:

Next, plug it all into our equation up above.

### Example Question #4 : How To Find The Area Of A Trapezoid

The above diagram shows Rectangle , with midpoint  of .

The area of Quadrilateral  is . Evaluate .

Explanation:

The easiest way to see this problem is to note that Quadrilateral  has as its area that of Rectangle  minus that of .

The area of Rectangle  is its length multiplied by its width:

is the midpoint of , so  has as its base and height  and , respectively;

its area is half their product, or

, so

### Example Question #1 : Trapezoids

The perimeter of the following trapezoid is equal to 23 cm. Solve for . (Figure not drawn to scale.)