All ISEE Middle Level Quantitative Resources
Example Questions
Example Question #1 : How To Find The Area Of A Triangle
A triangle has base 80 inches and area 4,200 square inches. What is its height?
Use the area formula for a triangle, setting :
inches
Example Question #1 : How To Find The Area Of A Triangle
The sum of the lengths of the legs of an isosceles right triangle is one meter. What is its area in square centimeters?
It is impossible to determine the area from the information given
The legs of an isosceles right triangle have equal length, so, if the sum of their lengths is one meter, which is equal to 100 centimeters, each leg measures half of this, or
centimeters.
The area of a triangle is half the product of its height and base; for a right triangle, the legs serve as height and base, so the area of the triangle is
square centimeters.
Example Question #11 : Triangles
The above figure depicts Square .
,
, and
are the midpoints of
,
, and
, respectively.
has area
. What is the area of Square
?
Since ,
, and
are the midpoints of
,
, and
, if we call
the length of each side of the square, then
The area of is half the product of the lengths of its legs:
The area of the square is the square of the length of a side, which is . This is eight times the area of
, so the correct choice is
Example Question #1 : How To Find The Area Of A Triangle
Which of the following is the greater quantity?
(a) The area of the above triangle
(b) 800
(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
(b) is the greater quantity
The area of a right triangle is half the product of the lengths of its legs, which here are 25 and 60. So
which is less than 800.
Example Question #252 : Geometry
The above figure gives the lengths of the three sides of the triangle in feet. Give its area in square inches.
The area of a right triangle is half the product of the lengths of its legs, which here are feet and
feet.
Multiply each length by 12 to convert to inches - the lengths become and
. The area in square inches is therefore
square inches.
Example Question #12 : Triangles
Figure NOT drawn to scale
Square has area 1,600.
;
. Which of the following is the greater quantity?
(a) The area of
(b) The area of
(b) is the greater quantity
(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
Square has area 1,600, so the length of each side is
.
Since ,
Therefore, .
has as its area
;
has as its area
.
Since and
, it follows that
and
has greater area than
.
Example Question #241 : Plane Geometry
Figure NOT drawn to scale.
In the above diagram, Square has area 400. Which is the greater quantity?
(a) The area of
(b) The area of
(a) and (b) are equal
It is impossible to determine which is greater from the information given
(a) is the greater quantity
(b) is the greater quantity
(b) is the greater quantity
Square has area 400, so its common sidelength is the square root of 400, or 20. Therefore,
.
The area of a right triangle is half the product of the lengths of its legs.
has legs
and
, so its area is
.
has legs
and
, so its area is
.
has the greater area.
Example Question #2 : How To Find The Area Of A Triangle
Figure NOT drawn to scale
The above diagram depicts Parallelogram . Which is the greater quantity?
(a) The area of
(b) The area of
(a) and (b) are equal
(a) is the greater quantity
It is impossible to determine which is greater from the information given
(a) and (b) are equal
Opposite sides of a parallelogram have the same measure, so
Base of
and base
of
have the same length; also, as can be seen below, both have the same height, which is the height of the parallelogram.
Therefore, the areas of and
have the same area -
.
Example Question #2 : How To Find The Area Of A Triangle
Refer to the above figure. Which is the greater quantity?
(a) The perimeter of the triangle
(b) 3 feet
(a) and (b) are equal
(a) is the greater quantity
(b) is the greater quantity
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
inches.
3 feet are equivalent to inches, so this is the greater quantity.
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All ISEE Middle Level Quantitative Resources
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