ISEE Middle Level Quantitative : Geometry
Study concepts, example questions & explanations for ISEE Middle Level Quantitative
All ISEE Middle Level Quantitative Resources
Example Questions
Example Question #4 : How To Find The Area Of A Triangle
Figure NOT drawn to scale.
In the above diagram, Square 
(a) The area of
(b) The area of
(a) is the greater quantity
It is impossible to determine which is greater from the information given
(a) and (b) are equal
(b) is the greater quantity
(b) is the greater quantity
Square 
The area of a right triangle is half the product of the lengths of its legs.
Example Question #4 : How To Find The Area Of A Triangle
Figure NOT drawn to scale
The above diagram depicts Parallelogram 
(a) The area of
(b) The area of
It is impossible to determine which is greater from the information given
(a) is the greater quantity
(a) and (b) are equal
(a) and (b) are equal
Opposite sides of a parallelogram have the same measure, so
Base 
Therefore, the areas of 
Example Question #261 : Geometry
Refer to the above figure. Which is the greater quantity?
(a) The perimeter of the triangle
(b) 3 feet
(b) is the greater quantity
(a) is the greater quantity
(a) and (b) are equal
It is impossible to determine which quantity is the greater from the information given
(b) is the greater quantity
The perimeter of the triangle - the sum of the lengths of its sides - is
3 feet are equivalent to 
Example Question #251 : Plane Geometry
Which is the greater quantity?
(a) 370 meters
(b) 3,700 centimeters
It is impossible to determine which is greater from the information given
(b) is the greater quantity
(a) is the greater quantity
(a) and (b) are equal
(a) is the greater quantity
One meter is equivalent to 100 centimeters, so 370 meters can be converted to centimeters by multiplying by 100:
370 meters are equal to 37.000 centimeters and is the greater quantity.
Example Question #252 : Plane Geometry
Which is the greater quantity?
(a) 4.8 kilometers
(b) 4,800 meters
(a) and (b) are equal
(a) is the greater quantity
It is impossible to determine which is greater from the information given
(b) is the greater quantity
(a) and (b) are equal
One kilometer is equal to 1,000 meters, so convert 4.8 kilometers to meters by multiplying by 1,000:
The two quantities are equal.
Example Question #3 : How To Find Length Of A Line
A regular pentagon has perimeter 1 yard. Give the length of one side.
A regular pentagon has five sides of equal length. The perimeter, which is the sum of the lengths of these sides, is one yard, which is equal to 36 inches. Therefore, the length of one side is
Example Question #253 : Plane Geometry
A regular hexagon has perimeter 8 feet. Give the length of one side.
24 inches
18 inches
16 inches
12 inches
16 inches
The perimeter can be converted from feet to inches by multiplying by conversion factor 12 {inches per foot):
A regular hexagon has six sides of equal length. Divide this perimeter by 6 to obtain the length of each side:
Example Question #1 : Solid Geometry
Which is the greater quantity?
(a) The sidelength of a cube with surface area
(b) The sidelength of a cube with volume
(a) and (b) are equal
(a) is greater
It is impossible to tell from the information given
(b) is greater
(a) and (b) are equal
(a) A cube has six faces, each a square. Since the surface area of this cube is 
(b) The volume of a cube is the cube of its sidelength, so we take the cube root of the volume of this cube to get the sidelength:
The cubes have the same sidelength.
Example Question #2 : Solid Geometry
Which is the greater quantity?
(a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters
(b) The volume of a cube with sidelength 300 millimeters
It is impossible to tell from the information given
(a) is greater
(b) is greater
(a) and (b) are equal
(a) and (b) are equal
(a) The volume of the prism is the product of its length, its width, and its height:
(b) The volume of the cube is the cube of its sidelength. We restate 300 millimeters as 30 centimeters, and cube this:
The volumes are equal.
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