How to find the area of a parallelogram - ISEE Upper Level (grades 9-12) Quantitative Reasoning
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In the above parallelogram, 
is acute. Which is the greater quantity?
(A) The area of the parallelogram
(B) 120 square inches
In the above parallelogram,
(A) The area of the parallelogram
(B) 120 square inches
Since 
is acute, a right triangle can be constructed with an altitude as one leg and a side as the hypotenuse, as is shown here. The height of the triangle must be less than its sidelength of 8 inches.
The height of the parallelogram must be less than its sidelength of 8 inches.
The area of the parallelogram is the product of the base and the height - which is 
Therefore,
(B) is greater.
Since
The height of the parallelogram must be less than its sidelength of 8 inches.
The area of the parallelogram is the product of the base and the height - which is
Therefore,
(B) is greater.
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Parallelogram A is below:
Parallelogram B is below:
Note: These figures are NOT drawn to scale.
Refer to the parallelograms above. Which is the greater quantity?
(A) The area of parallelogram A
(B) The area of parallelogram B
Parallelogram A is below:
Parallelogram B is below:
Note: These figures are NOT drawn to scale.
Refer to the parallelograms above. Which is the greater quantity?
(A) The area of parallelogram A
(B) The area of parallelogram B
The area of a parallelogram is the product of its height and its base; its slant length is irrelevant. Both parallelograms have the same height (8 inches) and the same base (1 foot, or 12 inches), so they have the same areas.
The area of a parallelogram is the product of its height and its base; its slant length is irrelevant. Both parallelograms have the same height (8 inches) and the same base (1 foot, or 12 inches), so they have the same areas.
Compare your answer with the correct one above
Figure NOT drawn to scale
The above figure shows Rhombus 
; 
and 
are midpoints of their respective sides. Rectangle 
has area 150.
Give the area of Rhombus 
.
Figure NOT drawn to scale
The above figure shows Rhombus
Give the area of Rhombus
A rhombus, by definition, has four sides of equal length. Therefore, 
. Also, since 
and 
are the midpoints of their respective sides,
We will assign 
to the common length of the four half-sides of the rhombus.
Also, both 
and 
are altitudes of the rhombus; the are congruent, and we will call their common length 
(height).
The figure, with the lengths, is below.
Rectangle 
has dimensions 
and 
; its area, 150, is the product of these dimensions, so
The area of the entire Rhombus 
is the product of its height 
and the length of a base 
, so
.
A rhombus, by definition, has four sides of equal length. Therefore,
We will assign
Also, both
The figure, with the lengths, is below.
Rectangle
The area of the entire Rhombus
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