ISEE Middle Level Math : Geometry
Study concepts, example questions & explanations for ISEE Middle Level Math
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Example Questions
Example Question #12 : Rectangles
A rectangular prism has length 24 inches, width 18 inches, and height 15 inches. Give its surface area in square feet.
Divide each dimension in inches by 12 to convert from inches to feet:
Now, substitute in the surface area formula:
Example Question #72 : Quadrilaterals
The area of a rectangle with a length of 
The area of a rectangle is the product of length and width:
Example Question #71 : Quadrilaterals
Give the area of a rectangle with a length of 
We know that:
where:
So we can write:
Example Question #23 : Geometry
A rectangular table has a length of 
We know that:
where:
So we can write:
Example Question #104 : Plane Geometry
The length of a rectangle is three times longer than its width. If the width of the rectangle is 
The length of the rectangle would be:
We know that:
where:
So we can write:
Example Question #173 : Plane Geometry
Which of the following is the area of a rectangle with a width of 4 feet and a length that is twice the width?
The area of a rectangle is found by multiplying the width by the length.
We know that the width is 4 feet and the the length must be twice the width. Multiply the width by 2 to find the length.
Multiply the length and width to find the area.
Example Question #331 : Ssat Middle Level Quantitative (Math)
Jeff decided to build a play area for his guinea pigs. The play area would be an enclosure 6 feet long, 2 feet wide, and 2 feet tall. In cubic feet, how big is the play area?
The cubic feet of an area is found by multiping the length times the width times the height. Given that the length is six feet, the width is two feet, and that the height is two feet, the total cubic area would be found using this equation:
Here is the equation with the appropriate numbers plugged in:
Therefore, 24 cubic feet is the correct answer.
Example Question #1 : Geometry
Jessica's blanket is 12 square feet. Lisa has a blanket that is half the size of Jessica's blanket. Which of the following are possible dimensions of Lisa's blanket?
The area of a rectangle if found by multiplying the length times the width. Here, we know that Lisa's blanket is half the area of Jessica's blanket. Since Jessica's blanket is 12 square feet, that means that Lisa's blanket must be 6 square feet.
The only length and width values that give us 6 square feet when multiplied by one another are 3 feet by 2 feet. This is therefore the correct answer.
Example Question #81 : Quadrilaterals
Note: Figure NOT drawn to scale.
What percent of the above figure is red?
The correct answer is not given among the other choices.
The correct answer is not given among the other choices.
The large rectangle has length 80 and width 40, and, consequently, area
The white region is a rectangle with length 30 and width 20, and, consequently, area
The red region, therefore, has area 
The red region is
of the large rectangle.
This is not one of the choices.
Example Question #21 : Rectangles
Note: Figure NOT drawn to scale.
Refer to the above diagram. Give the ratio of the area of the red region to that of the white region.
The correct answer is not given among the other choices.
The large rectangle has length 80 and width 40, and, consequently, area
The white region is a rectangle with length 30 and width 20, and, consequently, area
The red region, therefore, has area 
The ratio of the area of the red region to that of the white region is
That is, 13 to 3.
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