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ISEE Lower Level Quantitative : Geometry

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

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All ISEE Lower Level Quantitative Resources

20 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find A Parallelogram On A Coordinate Plane

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The parallelogram shown above has a height of and a base of length . Find the area of the parallelogram.

Possible Answers:

square units

Correct answer:

square units

Explanation:

To find the area of the parallelogram apply the formula: $A=base\times height$

Since, the paralleogram has a base of and a height of the solution is:
$A=5\times4=20$

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Example Question #1 : Coordinate Geometry

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The parallelogram shown above has a height of and a base of length . Find the perimeter of the parallelogram.

Possible Answers:

$P=(\sqrt{20}+5)$

$P=2(\sqrt{20}+4)$

p=2(20+5)

$P=2(\sqrt{20}+5)$

Correct answer:

$P=2(\sqrt{20}+5)$

Explanation:

In order to find the correct perimeter of the parallelogram apply the formula: P=2(a+b) , where the length of one of the diagonal sides and the length of the base.

In order to find the length of side , apply the formula: a^2+b^2=C^2 . By drawing an altitude from point (4,4) to (4,0) , a right triangle is formed with a base that has a length of and a height of .

Thus, the solution is:
a^2 +b^2=c^2
2^2+4^2= length of side a^2
4+16=20
a^2=20
$a=\sqrt{20}$

Therefore,

$P=2(\sqrt{20}+b)$
b=5
$P=2(\sqrt{20}+5)$

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Example Question #1 : How To Find A Parallelogram On A Coordinate Plane

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Identify the coordinate points for the parallelogram that is shown above.

Possible Answers:

(2,-2),(1,2),(3,2),(2,-1)

(-2,-2),(1,2),(3,2),(2,-1)

(-2,-1), (-1,2), (3,2), (2,-1)

(-2,1), (-1,2), (-3,-2), (-2,-1)

Correct answer:

(-2,-1), (-1,2), (3,2), (2,-1)

Explanation:

In order to identify the coordinate points for this parallelogram, notice that there must be two different pairs of coordinates with the same values.

Thus, the parallelogram has coordinate points: (-2,-1), (-1,2), (3,2), (2,-1)

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Example Question #2 : Coordinate Geometry

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What is the area of the parallelogram shown above?

Possible Answers:

square units

Correct answer:

square units

Explanation:

To find the area of the parallelogram that is shown, apply the formula: $A=base\times height$
Since the parallelogram has a base of and a height of the solution is:
$A=4\times 3=12$

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Example Question #5 : Coordinate Geometry

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Given that the above parallelogram has base sides with a length of and diagonal sides with a length of $\sqrt{10}$ what is the perimeter of the parallelogram?

Possible Answers:

$P=2(\sqrt{10}-4)$

$P=(\sqrt{10}+4)$

P=2(10+4)

$P=2(\sqrt{10}+4)$

$P=2(\sqrt{10}+3)$

Correct answer:

$P=2(\sqrt{10}+4)$

Explanation:

In order to find the perimeter of the parallelogram apply the formula: P=2(a+b) , where the length of one diagonal side and the length of one base.

In this problem, $a=\sqrt{10}$ and b= 4 .
Thus, the correct answer is: $P=2(\sqrt{10}+4)$

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Example Question #1 : Coordinate Geometry

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Identify the coordinate points for the parallelogram shown above.

Possible Answers:

(2,0), (4,4), (7,0), (9,4)

(2,1), (4,4), (7,0), (9,-4)

(-2,0), (4,4), (7,3), (9,4)

(2,5), (4,0), (7,1), (9,3)

Correct answer:

(2,0), (4,4), (7,0), (9,4)

Explanation:

In order to identify the coordinate points for this parallelogram, notice that there must be two different pairs of coordinates with the same values.

Thus, the correct set of coordinates is:
(2,0), (4,4), (7,0), (9,4)

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Example Question #1 : How To Find A Rectangle On A Coordinate Plane

A shape is plotted on a coordinate axis. The endpoints are $(2,0), (9,0), (2,4), and\ (9,4)$ . What shape is it?

Possible Answers:

Trapezoid

Rectangle

Parallelogram

Square

Triangle

Correct answer:

Rectangle

Explanation:

Plot the points on a coordinate axis. Once it's graphed, you can see that there are two pairs of congruent, or equal, sides. The shape that best fits these characteristics is a rectangle.

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Example Question #2 : How To Find A Rectangle On A Coordinate Plane

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Rectangle $\small ABCD$ has coordinates: $\small A(-4,-3)$ , $\small B(-4,1)$ , $\small C(3,1)$ , $\small D(3,-3)$ . Find the area of rectangle $\small ABCD$ .

Possible Answers:

$\small 28$ square units

$\small 11$ square units

$\small 32$ square units

$\small 26$ square units

Correct answer:

$\small 28$ square units

Explanation:

In order to find the area of rectangle $\small ABCD$ apply the formula: $\small A=width\times length$

Since rectangle $\small ABCD$ has a width of $\small 7$ and a length of $\small 4$ the solution is:

$\small A=7\times4=28$ square units

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Example Question #2 : Coordinate Geometry

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Rectangle $\small ABCD$ has coordinates: $\small A(-4,-3)$ , $\small B(-4,1)$ , $\small C(3,1)$ , $\small D(3,-3)$ . What is the perimeter?

Possible Answers:

$\small 22$

$\small 11$

$\small 28$

$\small 21$

$\small 23$

Correct answer:

$\small 22$

Explanation:

To find the perimeter of rectangle $\small ABCD$ , apply the formula: $\small p=2(width)+2(length)$

Thus, the solution is:

$\small p=2(7)+2(4)$
$\small p=14+8$
$\small p=22$

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Example Question #1 : How To Find A Rectangle On A Coordinate Plane

Rectangle ABCD has coordinate points: A(-2,2) , B(-2,4) , C(2,4) , D(2,2) . Find the area of rectangle ABCD .

Possible Answers:

square units

Correct answer:

square units

Explanation:

The area of rectangle ABCD can be found by multiplying the width and length of the rectangle.

To find the length of the rectangle compare the x values of two of the coordinates:

Since A(-2,2), C(2,4) the length is 2-(-2)=4 .

To find the width of the rectangle we need to look at the y coordinates of two of the points.

Since A(-2,2), C(2,4) the width is 4-2=2 .

The solution is:

$A=w\times l$
$A=4\times2=8$

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All ISEE Lower Level Quantitative Resources

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ISEE Lower Level Quantitative : Geometry

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

All ISEE Lower Level Quantitative Resources

Example Questions

Example Question #1 : How To Find A Parallelogram On A Coordinate Plane

Example Question #1 : Coordinate Geometry

Example Question #1 : How To Find A Parallelogram On A Coordinate Plane

Example Question #2 : Coordinate Geometry

Example Question #5 : Coordinate Geometry

Example Question #1 : Coordinate Geometry

Example Question #1 : How To Find A Rectangle On A Coordinate Plane

Example Question #2 : How To Find A Rectangle On A Coordinate Plane

Example Question #2 : Coordinate Geometry

Example Question #1 : How To Find A Rectangle On A Coordinate Plane

All ISEE Lower Level Quantitative Resources

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