Trapezoids

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ISEE Middle Level Quantitative Reasoning › Trapezoids

Questions 1 - 10
1

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 arms are 1.5 feet, what is the perimeter 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 arms are 1.5 feet, what is the perimeter of the base of your new bookshelf?

To find the perimeter of a bookshelf, we need to add up the lengths of the sides.

We know the two bases, we just need to add the lengths of the arms.

So, our answer is 8ft

2

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 arms are 1.5 feet, what is the perimeter 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 arms are 1.5 feet, what is the perimeter of the base of your new bookshelf?

To find the perimeter of a bookshelf, we need to add up the lengths of the sides.

We know the two bases, we just need to add the lengths of the arms.

So, our answer is 8ft

3

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.

So our answer is:

4

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.

So our answer is:

5

Find the perimeter of the trapezoid:
Question_12

Explanation

The perimeter of any shape is equal to the sum of the lengths of its sides:

6

Find the perimeter of the trapezoid:
Question_12

Explanation

The perimeter of any shape is equal to the sum of the lengths of its sides:

7

Trapezoid

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.

8

Trapezoid

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.

9

Rectangles 3

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

The area of Quadrilateral is

, so

10

Rectangles 3

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

The area of Quadrilateral is

, so

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