ISEE Lower Level Math : Geometry

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

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Example Questions

Example Question #41 : Geometry

Robert needs to determine the area of his rectangular wall in order to buy the proper amount of paint at the store. When he measures his wall he determines that it is 12 feet high and 20 feet wide. If one can of paint covers 40 square feet of wall, how many cans of paint does Robert need?

Possible Answers:

\(\displaystyle 3\)

\dpi{100} 4\(\displaystyle \dpi{100} 4\)

\dpi{100} 6\(\displaystyle \dpi{100} 6\)

\dpi{100} 8\(\displaystyle \dpi{100} 8\)

\dpi{100} 7\(\displaystyle \dpi{100} 7\)

Correct answer:

\dpi{100} 6\(\displaystyle \dpi{100} 6\)

Explanation:

Find the area of the wall - \dpi{100} 12\times 20=240\(\displaystyle \dpi{100} 12\times 20=240\)

Divide \dpi{100} 240\div 40=6\(\displaystyle \dpi{100} 240\div 40=6\)

6 cans of paint. 

Example Question #9 : How To Find The Area Of A Rectangle

What is the area of a rectangle with a length of \(\displaystyle \small 5\) feet and a width of \(\displaystyle \small 25\) feet? 

Possible Answers:

\(\displaystyle \small 30\) square feet

\(\displaystyle 250\) square feet

\(\displaystyle \small 125\) square feet

\(\displaystyle \small 60\) square feet

\(\displaystyle \small 100\) square feet

Correct answer:

\(\displaystyle \small 125\) square feet

Explanation:

To find the area of a rectangle, multiply the length by the width.

\(\displaystyle \small 5\times25=125\)

Example Question #21 : Plane Geometry

Joe has a rectangular poster that is 3 feet long and 2 feet wide. What is the area of the poster?

Possible Answers:

\(\displaystyle 6\ \text{ft}^2\)

\(\displaystyle 5\ \text{ft}^2\)

\(\displaystyle 8\ \text{ft}^2\)

\(\displaystyle 10\ \text{ft}^2\)

\(\displaystyle 4\ \text{ft}^2\)

Correct answer:

\(\displaystyle 6\ \text{ft}^2\)

Explanation:

The area of a rectangle is found by multiping the length times the width. Given that the length is 3 feet, the width is 2 feet, the total cubic area would be found using this equation:

\(\displaystyle \text{length}\times \text{width} = \text{area}\)

Here is the equation with the appropriate numbers plugged in from the question:

\(\displaystyle 3\ \text{ft}\times2\ \text{ft}=6\ \text{ft}^2\)

6 square feet, or \(\displaystyle 6\ \text{ft}^2\) is the correct answer. 

Example Question #22 : Plane Geometry

Leslie has a blanket that is \(\displaystyle 14\ \text{ft}^2\) in area. Jen has a blanket that is half the size of Leslie's blanket. How big is Jen's blanket?

Possible Answers:

\(\displaystyle 6\ \text{ft}^2\)

\(\displaystyle 12\ \text{ft}^2\)

\(\displaystyle 7\ \text{ft}^2\)

\(\displaystyle 24\ \text{ft}^2\)

\(\displaystyle 8\ \text{ft}^2\)

Correct answer:

\(\displaystyle 7\ \text{ft}^2\)

Explanation:

If Jen's blanket is half as big as Leslie's blanket, and Leslie's blanket is \(\displaystyle 14\ \text{ft}^2\), then we need to divide by 2 to find the area of Jen's blanket.

\(\displaystyle 14\ \text{ft}^2\div2=7\ \text{ft}^2\)

The area of Jen's blanket is \(\displaystyle 7\ \text{ft}^2\).

Example Question #23 : Plane Geometry

What is the area (in square feet) of a rectangle with a length of \(\displaystyle 7\) feet and a width of \(\displaystyle 6\) feet?

Possible Answers:

\(\displaystyle 49\ \text{ft}^2\)

\(\displaystyle 46\ \text{ft}^2\)

\(\displaystyle 38\ \text{ft}^2\)

\(\displaystyle 42\ \text{ft}^2\)

\(\displaystyle 47\ \text{ft}^2\)

Correct answer:

\(\displaystyle 42\ \text{ft}^2\)

Explanation:

The area of a rectangle is calculated by multiplying length times width.

\(\displaystyle A=l\times w\)

Given that the width is 6 feet and the height is 7, the product of 6 and 7 is 42.

\(\displaystyle A=6\ \text{ft}\times 7\ \text{ft}\)

\(\displaystyle A=42\ \text{ft}^2\)

Therefore, 42 is the correct answer. 

Example Question #24 : Plane Geometry

If the area of a rectangle is 28 square inches and its width is 4 inches, what is the length in inches?

Possible Answers:

None of these

\(\displaystyle 8\)

\(\displaystyle 7\)

\(\displaystyle 9\)

\(\displaystyle 6\)

Correct answer:

\(\displaystyle 7\)

Explanation:

The area of a rectangle is equal to the width multiplied by the length, or:

\(\displaystyle A=l\times w\)

If the area of a rectangle is 28 inches and the width is 4 inches, then plugging this into the equation we would get:

\(\displaystyle 28=l\times4\)

\(\displaystyle 28=4l\)

Divide both sides by 4 to solve.

\(\displaystyle 28\div4=4l\div4\)

\(\displaystyle 7=l\)

Example Question #25 : Plane Geometry

If a rectangle has an area of 18, which of the following are possible dimensions of the length and width?

Possible Answers:

\(\displaystyle l=9,\ w=2\)

None of these

\(\displaystyle l=4,\ w=3\)

\(\displaystyle l=8,\ w=2\)

\(\displaystyle l=5,\ w=3\)

Correct answer:

\(\displaystyle l=9,\ w=2\)

Explanation:

If the area of the rectangle is 18, that means that the length and the width, when multiplied together, should equal 18.

\(\displaystyle A=l\times w=18\)

The only numbers from the answer choices that would result in the product of 18 are 9 by 2, which is therefore the correct answer. 

\(\displaystyle l=9,\ w=2\)

\(\displaystyle 9\times2=18\)

Example Question #26 : Plane Geometry

Ben is making a sandbox with a width of 4 feet and a length of 6 feet. What is the area of the sandbox?

Possible Answers:

\(\displaystyle 24\ \text{ft}^2\)

\(\displaystyle 42\ \text{ft}^2\)

\(\displaystyle 36\ \text{ft}^2\)

\(\displaystyle 22\ \text{ft}^2\)

\(\displaystyle 18\ \text{ft}^2\)

Correct answer:

\(\displaystyle 24\ \text{ft}^2\)

Explanation:

The area of a rectangle is the width times the length.

\(\displaystyle A=w\times l\)

The width is 4 feet and the length is 6 feet. Because 4 times 6 is 24, the area is 24 square feet. 

\(\displaystyle A=4\text{ft}\times6\text{ft}\)

\(\displaystyle A=24\ \text{ft}^2\)

Example Question #27 : Plane Geometry

Jerry has a mat with an area of 20 square feet and a length of 5 feet. What is the width of the mat in inches?

Possible Answers:

\(\displaystyle 20\text{in}\)

\(\displaystyle 24\text{in}\)

\(\displaystyle 4\text{in}\)

None of these

\(\displaystyle 48\text{in}\)

Correct answer:

\(\displaystyle 48\text{in}\)

Explanation:

The area of a rectangle is the width times the length.

\(\displaystyle A=w\times l\)

Given that the area is 20 square feet and the length is 5 feet, the width would have to be 4 feet because 5 times 4 is 20.

\(\displaystyle 20\text{ft}^2=w\times5\text{ft}\)

\(\displaystyle w=\frac{20\text{ft}^2}{5\text{ft}}=4\text{ft}\)

Given that the question asks for the width in inches, 4 should be multiplied by 12 (as there are 12 inches in a foot).

\(\displaystyle 4\text{ft}\times12\text{inches per foot}=48\text{in}\)

This gives us a product of 48 inches, which is the width. 

Example Question #11 : How To Find The Area Of A Rectangle

If the length of a rectangle is 2r and the width of the rectangle is 3w, what is the area?

Possible Answers:

\(\displaystyle 6rw\)

\(\displaystyle 3(rw)^{2}\)

\(\displaystyle 6r\)

\(\displaystyle 5w\)

Correct answer:

\(\displaystyle 6rw\)

Explanation:

The area of a rectangle is found by multiplying the length by the width. Given that the length is 2r and that the length is 3w, the area will be the product of those numbers, which is \(\displaystyle 6rw\).

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