Trapezoids
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ISEE Middle Level Quantitative Reasoning › Trapezoids
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
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
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:
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:
Find the perimeter of the trapezoid:

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

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

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.

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.

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

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