ISEE Lower Level Quantitative : Geometry

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

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Example Questions

Example Question #301 : Geometry

How many square units make up the area of the shape below? 

Screen shot 2015 09 28 at 11.50.32 am

Possible Answers:

\(\displaystyle 3\textup { square units}\)

\(\displaystyle 1\textup { square unit}\)

\(\displaystyle 4\textup { square units}\)

\(\displaystyle 5\textup { square units}\)

\(\displaystyle 2\textup { square units}\)

Correct answer:

\(\displaystyle 5\textup { square units}\)

Explanation:

The shape is made up of unit squares. We can count the number of squares within the shape to find the area. 

There are \(\displaystyle 5\) squares within the shape. 

Example Question #11 : How To Find Perimeter

What is the length of a rectangular room with a perimeter of \(\displaystyle 42ft\) and a width of \(\displaystyle 7ft?\)

Possible Answers:

\(\displaystyle 28ft\)

\(\displaystyle 18ft\)

\(\displaystyle 12ft\)

\(\displaystyle 22ft\)

\(\displaystyle 14ft\)

Correct answer:

\(\displaystyle 14ft\)

Explanation:

\(\displaystyle P=2l+ 2w\)

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 42=2l+2(7)\)

\(\displaystyle 42=2l+14\)

Subtract \(\displaystyle 14\) from both sides

\(\displaystyle 42-14=2l+14-14\)

\(\displaystyle 28=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{28}{2}=\frac{2l}{2}\)

\(\displaystyle 14=l\)

Example Question #12 : How To Find Perimeter

What is the length of a rectangular room with a perimeter of \(\displaystyle 62ft\) and a width of \(\displaystyle 8ft?\)

 

Possible Answers:

\(\displaystyle 23ft\)

\(\displaystyle 37ft\)

\(\displaystyle 38ft\)

\(\displaystyle 46ft\)

\(\displaystyle 40ft\)

Correct answer:

\(\displaystyle 23ft\)

Explanation:

\(\displaystyle P=2l+ 2w\)

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 62=2l+2(8)\)

\(\displaystyle 62=2l+16\)

Subtract \(\displaystyle 16\) from both sides

\(\displaystyle 62-16=2l+16-16\)

\(\displaystyle 46=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{46}{2}=\frac{2l}{2}\)

\(\displaystyle 23=l\)

Example Question #13 : How To Find Perimeter

What is the length of a rectangular room with a perimeter of \(\displaystyle 92ft\) and a width of \(\displaystyle 21ft?\)

 

Possible Answers:

\(\displaystyle 25ft\)

\(\displaystyle 50ft\)

\(\displaystyle 30ft\)

\(\displaystyle 45ft\)

\(\displaystyle 40ft\)

Correct answer:

\(\displaystyle 25ft\)

Explanation:

\(\displaystyle P=2l+ 2w\)

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 92=2l+2(21)\)

\(\displaystyle 92=2l+42\)

Subtract \(\displaystyle 42\) from both sides

\(\displaystyle 92-42=2l+42-42\)

\(\displaystyle 50=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{50}{2}=\frac{2l}{2}\)

\(\displaystyle 25=l\)

Example Question #61 : Parallelograms

What is the length of a rectangular room with a perimeter of \(\displaystyle 59ft\) and a width of \(\displaystyle 17ft?\)

Possible Answers:

\(\displaystyle 15.5ft\)

\(\displaystyle 12ft\)

\(\displaystyle 12.5ft\)

\(\displaystyle 15ft\)

\(\displaystyle 25ft\)

Correct answer:

\(\displaystyle 12.5ft\)

Explanation:

\(\displaystyle P=2l+ 2w\)

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 59=2l+2(17)\)

\(\displaystyle 59=2l+34\)

Subtract \(\displaystyle 34\) from both sides

\(\displaystyle 59-34=2l+134-34\)

\(\displaystyle 25=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{25}{2}=\frac{2l}{2}\)

\(\displaystyle 12.5=l\)

Example Question #14 : How To Find Perimeter

What is the length of a rectangular room with a perimeter of \(\displaystyle 66ft\) and a width of \(\displaystyle 18ft?\)

 

Possible Answers:

\(\displaystyle 12ft\)

\(\displaystyle 13ft\)

\(\displaystyle 14ft\)

\(\displaystyle 11ft\)

\(\displaystyle 15ft\)

Correct answer:

\(\displaystyle 15ft\)

Explanation:

\(\displaystyle P=2l+ 2w\)

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 66=2l+2(18)\)

\(\displaystyle 66=2l+36\)

Subtract \(\displaystyle 36\) from both sides

\(\displaystyle 66-36=2l+36-36\)

\(\displaystyle 30=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{30}{2}=\frac{2l}{2}\)

\(\displaystyle 15=l\)

Example Question #63 : Parallelograms

What is the length of a rectangular room with a perimeter of \(\displaystyle 60ft\) and a width of \(\displaystyle 14ft?\)

Possible Answers:

\(\displaystyle 32ft\)

\(\displaystyle 26ft\)

\(\displaystyle 30ft\)

\(\displaystyle 18ft\)

\(\displaystyle 16ft\)

Correct answer:

\(\displaystyle 16ft\)

Explanation:

\(\displaystyle P=2l+ 2w\)

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 60=2l+2(14)\)

\(\displaystyle 60=2l+28\)

Subtract \(\displaystyle 28\) from both sides

\(\displaystyle 60-28=2l+28-28\)

\(\displaystyle 32=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{32}{2}=\frac{2l}{2}\)

\(\displaystyle 16=l\)

Example Question #22 : Squares

What is the length of a rectangular room with a perimeter of \(\displaystyle 40ft\) and a width of \(\displaystyle 6ft?\)

Possible Answers:

\(\displaystyle 16ft\)

\(\displaystyle 32ft\)

\(\displaystyle 14ft\)

\(\displaystyle 18ft\)

\(\displaystyle 28ft\)

Correct answer:

\(\displaystyle 14ft\)

Explanation:

\(\displaystyle P=2l+ 2w\)

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 40=2l+2(6)\)

\(\displaystyle 40=2l+12\)

Subtract \(\displaystyle 12\) from both sides

\(\displaystyle 40-12=2l+12-12\)

\(\displaystyle 28=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{28}{2}=\frac{2l}{2}\)

\(\displaystyle 14=l\)

Example Question #77 : Plane Geometry

What is the length of a rectangular room with a perimeter of \(\displaystyle 96ft\) and a width of \(\displaystyle 30ft?\)

Possible Answers:

\(\displaystyle 19ft\)

\(\displaystyle 20ft\)

\(\displaystyle 24ft\)

\(\displaystyle 18ft\)

\(\displaystyle 22ft\)

Correct answer:

\(\displaystyle 18ft\)

Explanation:

\(\displaystyle P=2l+ 2w\)

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 96=2l+2(30)\)

\(\displaystyle 96=2l+60\)

Subtract \(\displaystyle 60\) from both sides

\(\displaystyle 96-60=2l+60-60\)

\(\displaystyle 36=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{36}{2}=\frac{2l}{2}\)

\(\displaystyle 18=l\)

Example Question #64 : Parallelograms

What is the length of a rectangular room with a perimeter of \(\displaystyle 90ft\) and a width of \(\displaystyle 12ft\)

Possible Answers:

\(\displaystyle 55ft\)

\(\displaystyle 33ft\)

\(\displaystyle 22ft\)

\(\displaystyle 66ft\)

\(\displaystyle 44ft\)

Correct answer:

\(\displaystyle 33ft\)

Explanation:

\(\displaystyle P=2l+ 2w\)

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 90=2l+2(12)\)

\(\displaystyle 90=2l+24\)

Subtract \(\displaystyle 24\) from both sides

\(\displaystyle 90-24=2l+24-24\)

\(\displaystyle 66=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{66}{2}=\frac{2l}{2}\)

\(\displaystyle 33=l\)

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