ISEE Upper Level Math : Geometry
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Example Questions
Example Question #241 : Isee Upper Level (Grades 9 12) Mathematics Achievement
Find the perimeter of a square with a side length of 
A square has 4 equal sides.
Write the formula for the perimeter of a square.
Substitute the side length.
Evaluate the terms on the right.
The answer is:
Example Question #242 : Isee Upper Level (Grades 9 12) Mathematics Achievement
Your new friend has a very small, square-shaped dorm room. She tells you that it is only 225 square feet. Assuming this is true, what is the perimeter of her room?
Not enough information to solve the problem
Your new friend has a very small, square-shaped dorm room. She tells you that it is only 225 square feet. Assuming this is true, what is the perimeter of her room?
So, we need to find the perimeter of a square. First, we need to find the side length.
Let's begin with our formula for the area of a square:
where s is our side length and A is our area.
With this formula, we can solve for our side length by plugging in our area and square rooting both sides.
Now, we are close but not quite done. We need to multiply our side length by 4, because a square always has 4 equal sides.
Example Question #241 : Geometry
A square is made into a rectangle by increasing the width by 20% and decreasing the length by 20%. By what percentage has the area of the square changed?
increased by 20%
the area remains the same
decreased by 4%
decreased by 10%
decreased by 4%
The area decreases by 20% of 20%, which is 4%.
The easiest way to see this is to plug in numbers for the sides of the square. If we are using percentages, it is easiest to use factors of 10 or 100. In this case we will say that the square has a side length of 10.
10% of 10 is 1, so 20% is 2. Now we can just increase one of the sides by 2, and decrease another side by 2. So our rectangle has dimensions of 12 x 8 instead of 10 x 10.
The original square had an area of 100, and the new rectangle has an area of 96. So the rectangle is 4 square units smaller, which is 4% smaller than the original square.
Example Question #11 : Squares
Side 
Cannot be determined
To find the area of a quadrilateral, multiply length times width. In a square, since all sides are equal, 
Example Question #12 : Squares
If Amy is carpeting her living room, which meaures 
To find the area of the floor, multiply the length of the room by the width (which is the same forumla used to find the area of a square). The equation can be written:
Substitute 
Amy will need 
Example Question #2 : How To Find The Area Of A Square
A rectangle and a square have the same perimeter. The rectangle has length 
The perimeter of the rectangle is
This is also the perimeter of the square, so divide this by 
The area is the square of this, or 
Example Question #13 : Squares
Four squares have sidelengths 4 inches, 8 inches, 12 inches, and 16 inches. What is the average of their areas?
The areas of the four squares can be calculated by squaring their sidelengths. Add these areas, then divide by 4:
Example Question #14 : Squares
Which of the following is equal to the area of a square with sidelength 
Multiply the sidelength by 36 to convert from yards to inches:
Square this to get the area:
Example Question #15 : Squares
What is the area of a square in which the length of one side is equal to 
The area of a square is equal to the product of one side multiplied by another side. Therefore, the area will be equal to:
The next step is to convert the fractions being added together to a form in which they have a common denominator. This gives us:
Example Question #17 : Squares
One of the sides of a square on the coordinate plane has its endpoints at the points with coordinates 
The length of a segment with endpoints 
This is the length of one side of the square, so the area is the square of this, or 122.
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