ISEE Middle Level Math : Plane Geometry
Study concepts, example questions & explanations for ISEE Middle Level Math
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Example Questions
Example Question #11 : Geometry
Order the following from least area to greatest area:
Figure A: A rectangle with length 10 inches and width 14 inches.
Figure B: A square with side length 1 foot.
Figure C: A triangle with base 16 inches and height 20 inches.
Figure A has area 
Figure B has area 
Figure C has area 
The figures, arranged from least area to greatest, are A, B, C.
Example Question #2 : How To Find The Area Of A Rectangle
Give the surface area of the above box in square inches.
Use the surface area formula, substituting 
Example Question #2 : Area Of A Rectangle Or Square
The area of the following rectangle is 
The area of a rectangle can be found by multiplying the length by the width.
Example Question #161 : Plane Geometry
Give the area of the above rectangle in square feet.
Since 1 yard = 3 feet, multiply each dimension by 3 to convert from yards to feet:
Use the area formula, substituting 
Example Question #12 : Geometry
The ratio of the perimeter of one square to that of another square is 
For the sake of simplicity, we will assume that the second square has sidelength 1; Then its perimeter is 
The perimeter of the first square is 
The ratio of the areas is therefore 
Example Question #162 : Plane Geometry
The following question is about the Jones family wanting to buy square foot tiles for their rectangular basement. Their basement perimeter is 74 feet, with one of the sides being 15 feet long.
How many square foot titles are the Jones family needing to purchase in order to tile their basement?
From the given information we know that the perimeter of the rectangular basement is 74 feet. We also know that one side of the rectangular basement is 15 feet. This means that the opposite side is also 15 feet long because the equivalent opposite sides rule of rectangles. In order to find the lengths of our other two sides of the rectangle, we need to subtract our two 15 feet sides from the perimeters 74 feet.
We know that the last two sides have to add up to 44 feet. Since the rules of rectangles say opposite sides are equivalent, we must take 44 feet and divide by the 2 sides. So 44 divided by 2 is 22 feet, meaning each side must be 22 feet. After adding up all the sides we can confirm that our perimeter is 74 feet.
Now we know all the sides of the rectangle, we are able to move to the next step, finding the area. We must find the area, because the tiles are square feet. So in order to find the area we must take the length of the rectangle and multiply it to the width.
Knowing the area of the rectangular basement we also know how many tile are needed to fill the basement for the Jones family. It is exactly 330 square feet tile needed.
Example Question #1 : Rectangles
Which of the following is equal to the area of a rectangle with length 250 centimeters and width 140 centimeters?
Divide each dimension by 100 to convert centimeters to meters:
Multiply length by width:
Example Question #3 : Rectangles
A hectare is a unit of area equal to 10,000 square meters.
A rectangular plot of land measures 1,400 meters by 800 meters. Give the area of this plot in hectares.
Multiply length times width to get the area in square meters:
Divide by 10,000 to convert to hectares:
Example Question #5 : Rectangles
Which of the following is equal to the area of a rectangle with length 27 inches and width 15 inches?
Divide each dimension by 12 to convert from inches to feet:
Multiply length by width:
Example Question #163 : Plane Geometry
Which of the following is equal to the area of a rectangle with length 
Multiply each dimension by 12 to convert from feet to inches:
Now multiply this length and width to get the area:
All ISEE Middle Level Math Resources
