How to find the area of a parallelogram - SSAT Upper Level Quantitative
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A parallelogram has the base length of 
and the altitude of 
. Give the area of the parallelogram.
A parallelogram has the base length of
The area of a parallelogram is given by:
Where 
is the base length and 
is the corresponding altitude. So we can write:
The area of a parallelogram is given by:
Where
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A parallelogram has a base length of 
which is 3 times longer than its corresponding altitude. The area of the parallelogram is 12 square inches. Give the 
.
A parallelogram has a base length of
Base length is 
so the corresponding altitude is 
.
The area of a parallelogram is given by:
Where:
is the length of any base
is the corresponding altitude
So we can write:
Base length is
The area of a parallelogram is given by:
Where:
So we can write:
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The length of the shorter diagonal of a rhombus is 40% that of the longer diagonal. The area of the rhombus is 
. Give the length of the longer diagonal in terms of 
.
The length of the shorter diagonal of a rhombus is 40% that of the longer diagonal. The area of the rhombus is
Let 
be the length of the longer diagonal. Then the shorter diagonal has length 40% of this. Since 40% is equal to 
, 40% of 
is equal to 
.
The area of a rhombus is half the product of the lengths of its diagonals, so we can set up, and solve for 
, in the equation:
Let
The area of a rhombus is half the product of the lengths of its diagonals, so we can set up, and solve for
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The length of the shorter diagonal of a rhombus is two-thirds that of the longer diagonal. The area of the rhombus is 
square yards. Give the length of the longer diagonal, in inches, in terms of 
.
The length of the shorter diagonal of a rhombus is two-thirds that of the longer diagonal. The area of the rhombus is
Let be the length of the longer diagonal in yards. Then the shorter diagonal has length two-thirds of this, or 
.
The area of a rhombus is half the product of the lengths of its diagonals, so we can set up the following equation and solve for :
To convert yards to inches, multiply by 36:
Let
The area of a rhombus is half the product of the lengths of its diagonals, so we can set up the following equation and solve for
To convert yards to inches, multiply by 36:
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The longer diagonal of a rhombus is 20% longer than the shorter diagonal; the rhombus has area 
. Give the length of the shorter diagonal in terms of 
.
The longer diagonal of a rhombus is 20% longer than the shorter diagonal; the rhombus has area
Let 
be the length of the shorter diagonal. If the longer diagonal is 20% longer, then it measures 120% of the length of the shorter diagonal; this is
of 
, or 
.
The area of a rhombus is half the product of the lengths of its diagonals, so we can set up an equation and solve for :
Let
of
The area of a rhombus is half the product of the lengths of its diagonals, so we can set up an equation and solve for
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Which of the following shapes is NOT a quadrilateral?
Which of the following shapes is NOT a quadrilateral?
A quadrilateral is any two-dimensional shape with 
sides. The only shape listed that does not have 
sides is a triangle.
A quadrilateral is any two-dimensional shape with
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What other shape can a parallelogram be classified as?
What other shape can a parallelogram be classified as?
A parallelogram can not be classified as a square because a square has to have 
equal sides, but a parallelogram can have two different side lengths, as long as the opposite side lengths are equal.
A parallelogram can not be classified as a rectangle because a rectangle has to have 
angles, and a parallelogram does not.
A parallelogram can not be classified as a triangle because a parallelogram has to have 
sides and a triangle only has 
sides.
A parallelogram can not be classified as a rhombus because a rhombus has to have 
equal sides and a parallelogram does not.
A parallelogram has four sides, and all shapes with four sides are quadrilaterals.
A parallelogram can not be classified as a square because a square has to have
A parallelogram can not be classified as a rectangle because a rectangle has to have
A parallelogram can not be classified as a triangle because a parallelogram has to have
A parallelogram can not be classified as a rhombus because a rhombus has to have
A parallelogram has four sides, and all shapes with four sides are quadrilaterals.
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What is the main difference between a square and a rectangle?
What is the main difference between a square and a rectangle?
The only difference between a rectangle and a square is their side lengths. A square has to have 
equal side lengths, but the opposite side lengths of a rectangle only have to be equal.
The only difference between a rectangle and a square is their side lengths. A square has to have
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What two shapes can a square be classified as?
What two shapes can a square be classified as?
A square can also be a rectangle and a rhombus because a rectangle has to have at least 
sets of equal side lengths and a rhombus has to have 
equal side lengths, like a square, and at least 
sets of equal angles.
A square can also be a rectangle and a rhombus because a rectangle has to have at least
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What is the main difference between a triangle and a rectangle?
What is the main difference between a triangle and a rectangle?
Out of the choices given, the only characteristic used to describe shapes is the number of sides. A triangle has 
sides and a rectangle has 
sides.
Out of the choices given, the only characteristic used to describe shapes is the number of sides. A triangle has
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Which two shapes have to have 
right angles?
Which two shapes have to have
By definition, the only two quadrilaterals that have to have 
right angles, are the square and the rectangle.
By definition, the only two quadrilaterals that have to have
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Which of the shapes is NOT a quadrilateral?
Which of the shapes is NOT a quadrilateral?
A quadrilateral is a 
sided shape. The only shape listed that does not have 
sides is a hexagon, which has 
sides.
A quadrilateral is a
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Which of the following shapes is NOT a parallelogram?
Which of the following shapes is NOT a parallelogram?
A rectangle, square, and rhombus can all be classified as a parallelogram because each shape has opposite side lengths that are equal. A kite does not.
A rectangle, square, and rhombus can all be classified as a parallelogram because each shape has opposite side lengths that are equal. A kite does not.
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What is the difference between a trapezoid and a isosceles trapezoid?
What is the difference between a trapezoid and a isosceles trapezoid?
By definition, an isosceles trapezoid has to have 
equal base angles, but a trapezoid does not have to have equal angles.
By definition, an isosceles trapezoid has to have
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Which shape is NOT a quadrilateral?
Which shape is NOT a quadrilateral?
A quadrilateral has to have 
sides, a circle does not have any sides.
A quadrilateral has to have
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Figure NOT drawn to scale.
The above depicts Rhombus 
, which has perimeter 80. 
.
Give the area of Rhombus 
.
Figure NOT drawn to scale.
The above depicts Rhombus
Give the area of Rhombus
The area of any parallelogram is the product of the length of its base and that of a corresponding altitude. We can take 
as a base and perpendicular 
as an altitude.
All four sides of a rhombus have the same length, so we can find 
by dividing the perimeter - the sum of the lengths of the four sides - by 4:
Now multiply the lengths of this base and the altitude to get the area:
The area of any parallelogram is the product of the length of its base and that of a corresponding altitude. We can take
All four sides of a rhombus have the same length, so we can find
Now multiply the lengths of this base and the altitude to get the area:
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A parallelogram has the base length of and the altitude of . Give the area of the parallelogram.
A parallelogram has the base length of
The area of a parallelogram is given by:
Where is the base length and is the corresponding altitude. So we can write:
The area of a parallelogram is given by:
Where
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A parallelogram has a base length of which is 3 times longer than its corresponding altitude. The area of the parallelogram is 12 square inches. Give the .
A parallelogram has a base length of
Base length is so the corresponding altitude is .
The area of a parallelogram is given by:
Where:
is the length of any base
is the corresponding altitude
So we can write:
Base length is
The area of a parallelogram is given by:
Where:
So we can write:
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The length of the shorter diagonal of a rhombus is 40% that of the longer diagonal. The area of the rhombus is . Give the length of the longer diagonal in terms of .
The length of the shorter diagonal of a rhombus is 40% that of the longer diagonal. The area of the rhombus is
Let be the length of the longer diagonal. Then the shorter diagonal has length 40% of this. Since 40% is equal to , 40% of is equal to .
The area of a rhombus is half the product of the lengths of its diagonals, so we can set up, and solve for , in the equation:
Let
The area of a rhombus is half the product of the lengths of its diagonals, so we can set up, and solve for
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The length of the shorter diagonal of a rhombus is two-thirds that of the longer diagonal. The area of the rhombus is square yards. Give the length of the longer diagonal, in inches, in terms of .
The length of the shorter diagonal of a rhombus is two-thirds that of the longer diagonal. The area of the rhombus is
Let be the length of the longer diagonal in yards. Then the shorter diagonal has length two-thirds of this, or .
The area of a rhombus is half the product of the lengths of its diagonals, so we can set up the following equation and solve for :
To convert yards to inches, multiply by 36:
Let
The area of a rhombus is half the product of the lengths of its diagonals, so we can set up the following equation and solve for
To convert yards to inches, multiply by 36:
Compare your answer with the correct one above