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SSAT Upper Level Math : How to find the area of a parallelogram

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Example Questions

Example Question #81 : Areas And Perimeters Of Polygons

A parallelogram has the base length of and the altitude of 2t-1 . Give the area of the parallelogram.

Possible Answers:

2t^2+t

t^2

2t^2-t

t^2+t

2t^2

Correct answer:

2t^2-t

Explanation:

The area of a parallelogram is given by:

Area=ba

Where is the base length and is the corresponding altitude. So we can write:

Area=t(2t-1)=2t^2-t

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Example Question #2 : Area Of A Parallelogram

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 .

Possible Answers:

$6\sqrt{2}$

$6\sqrt{3}$

Correct answer:

Explanation:

Base length is so the corresponding altitude is $\frac{t}{3}$ .

The area of a parallelogram is given by:

Area=ba

Where:

is the length of any base
is the corresponding altitude

So we can write:

$12=t\times \frac{t}{3}\Rightarrow t\times t=12\times 3\Rightarrow t^2=36\Rightarrow t=6$

$t\times t=12\times 3$

$t^{2}=36$

t=6

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Example Question #2 : Area Of A Parallelogram

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 .

Possible Answers:

$\sqrt{\frac{5K}{2}}$

$\sqrt{5K}$

$K\sqrt{\frac{5}{2}}$

$\frac{1}{5}\sqrt{K}$

$K\sqrt{\frac{2}{5}}$

Correct answer:

$\sqrt{5K}$

Explanation:

Let be the length of the longer diagonal. Then the shorter diagonal has length 40% of this. Since 40% is equal to $\frac{40}{100 } = \frac{40 \div 20 }{100 \div 20 } = \frac{2}{5}$ , 40% of is equal to $\frac{2}{5}D$ .

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:

$\frac{1}{2} \cdot \frac{2}{5}D \cdot D = K$

$\frac{1}{5}D^{2}= K$

$5\cdot \frac{1}{5}D^{2}=5\cdot K$

$D^{2}=5K$

$D =\sqrt{5K}$

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Example Question #1 : Area Of A Parallelogram

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 .

Possible Answers:

$12\sqrt{ 3Q}$

$3\sqrt{ 3Q}$

$4\sqrt{ 3Q}$

$\sqrt{ 3Q}$

$36\sqrt{ 3Q }$

Correct answer:

$36\sqrt{ 3Q }$

Explanation:

Let be the length of the longer diagonal in yards. Then the shorter diagonal has length two-thirds of this, or $\frac{2}{3}D$ .

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 :

$\frac{1}{2} \cdot \frac{2}{3}D \cdot D = Q$

$\frac{1}{3}D ^{2} = Q$

$3\cdot \frac{1}{3}D ^{2} = 3 \cdot Q$

$D ^{2} = 3Q$

$D = \sqrt{3Q}$

To convert yards to inches, multiply by 36:

$\sqrt{ 3Q } \times 36 = 36\sqrt{ 3Q }$

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Example Question #2 : Area Of A Parallelogram

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 .

Possible Answers:

$\sqrt{15N}$

$\sqrt{5N}$

$\sqrt{ \frac{3N}{5}}$

$\sqrt{ \frac{5N}{3}}$

$\sqrt{ \frac{N}{5}}$

Correct answer:

$\sqrt{ \frac{5N}{3}}$

Explanation:

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

$\frac{120}{100} = \frac{120 \div 20}{100 \div 20} = \frac{6}{5}$

of , or $\frac{6}{5}D$ .

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 :

$\frac{1}{2} \cdot \frac{6}{5}D \cdot D = N$

$\frac{3}{5}D^{2} = N$

$\frac{5}{3} \cdot \frac{3}{5}D^{2} = \frac{5}{3} \cdot N$

$D^{2} = \frac{5N}{3}$

$D =\sqrt{ \frac{5N}{3}}$

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Example Question #1 : Understand Categories And Subcategories Of Two Dimensional Figures: Ccss.Math.Content.5.G.B.3

Which of the following shapes is NOT a quadrilateral?

Possible Answers:

Rhombus

Triangle

Kite

Rectangle

Square

Correct answer:

Triangle

Explanation:

A quadrilateral is any two-dimensional shape with sides. The only shape listed that does not have sides is a triangle.

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Example Question #2 : Understand Categories And Subcategories Of Two Dimensional Figures: Ccss.Math.Content.5.G.B.3

What is the main difference between a square and a rectangle?

Possible Answers:

Their side lengths

Their angle measurments

The sum of their angles

The number of sides they each have

Their color

Correct answer:

Their side lengths

Explanation:

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.

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Example Question #4 : Understand Categories And Subcategories Of Two Dimensional Figures: Ccss.Math.Content.5.G.B.3

What is the main difference between a triangle and a rectangle?

Possible Answers:

The area

The color

The number of sides

The length of the sides

The volume

Correct answer:

The number of sides

Explanation:

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.

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Example Question #5 : Understand Categories And Subcategories Of Two Dimensional Figures: Ccss.Math.Content.5.G.B.3

Which two shapes have to have right angles?

Possible Answers:

Rectangle and Rhombus

Rectangle and Parallelogram

Square and Rectangle

Square and Rhombus

Square and Parallelogram

Correct answer:

Square and Rectangle

Explanation:

By definition, the only two quadrilaterals that have to have right angles, are the square and the rectangle.

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Example Question #4 : Understand Categories And Subcategories Of Two Dimensional Figures: Ccss.Math.Content.5.G.B.3

Which of the shapes is NOT a quadrilateral?

Possible Answers:

Trapezoid

Hexagon

Rectangle

Rhombus

Square

Correct answer:

Hexagon

Explanation:

A quadrilateral is a sided shape. The only shape listed that does not have sides is a hexagon, which has sides.

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SSAT Upper Level Math : How to find the area of a parallelogram

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #81 : Areas And Perimeters Of Polygons

Example Question #2 : Area Of A Parallelogram

Example Question #2 : Area Of A Parallelogram

Example Question #1 : Area Of A Parallelogram

Example Question #2 : Area Of A Parallelogram

Example Question #1 : Understand Categories And Subcategories Of Two Dimensional Figures: Ccss.Math.Content.5.G.B.3

Example Question #2 : Understand Categories And Subcategories Of Two Dimensional Figures: Ccss.Math.Content.5.G.B.3

Example Question #4 : Understand Categories And Subcategories Of Two Dimensional Figures: Ccss.Math.Content.5.G.B.3

Example Question #5 : Understand Categories And Subcategories Of Two Dimensional Figures: Ccss.Math.Content.5.G.B.3

Example Question #4 : Understand Categories And Subcategories Of Two Dimensional Figures: Ccss.Math.Content.5.G.B.3

All SSAT Upper Level Math Resources

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