SSAT Upper Level Math : Geometry
Study concepts, example questions & explanations for SSAT Upper Level Math
All SSAT Upper Level Math Resources
Example Questions
Example Question #2 : How To Find The Perimeter Of A Square
The length of each side of the square is 
To find the perimter of a square, multiply the side length by 4.
Example Question #3 : How To Find The Perimeter Of A Square
A square has a diagonal length of 
Since the diagonal of a squre is also the hypotenuse of a right triangle whose legs are the sides of the square, use the Pythagorean Theorem to find out the lengths of the sides of the square.
Now, multiply the side length by 4 to find the perimter.
Example Question #4 : How To Find The Perimeter Of A Square
The area of a square is 
To figure out the perimeter, we need to first find the length of 1 side of the square.
Find the length of a side of the square using the information given about the area.
Now, multiply the side length by 4.
Example Question #8 : How To Find The Perimeter Of A Square
The diagonal of a square is 
The diagonal of a square is also the hypotenuse of a triangle whose legs are two sides of the square. Using that information, we can find the length of each side of the square.
Now, multiply the side length by 4 to find the perimeter.
Example Question #9 : How To Find The Perimeter Of A Square
The track at Harriet Beecher Stowe High School is a perfect square of with diagonal 600 feet, and is shown in the above figure. Beginning at point A, Corinne runs around the track clockwise three complete times, then contunes to run until she reaches point B. Which of the following comes closest to the distance Corinne runs?
You will need to know that 
A square with diagonal 600 feet will have as its sidelength
If Corinne runs the entire perimeter of the square three times, and then runs on to Point B, she will run this distance a total of about 
Divide by 5,280 to convert to miles:
The closest response is 1 mile.
Example Question #6 : How To Find The Perimeter Of A Square
The track at Frederick Douglass High School is a perfect square of with diagonal 400 feet, and is shown in the above figure. Julia wants to run around the track for one mile. If Julia starts at point A and runs clockwise, where will she be after she has run for a mile?
A hint:
A square with diagonal 400 feet will have as its sidelength
Julia wants to run one mile, or 5,280 feet; this will be
Julia will run around the track four times, then another 2 sidelengths. She will then run seven-tenths of the length of the "bottom" side, ending up at point D.
Example Question #1 : How To Find The Area Of A Square
The volume of a cube is 1,000 cubic centimeters. Using the conversion factor 2.5 centimeters = 1 inch, give its surface area in square inches, rounding to the nearest square inch.
96 square inches
144 square inches
100 square inches
108 square inches
75 square inches
96 square inches
The surface area of a cube is six times the square of its sidelength, so we find the sidelength. This is the cube root of volume 1,000, so
To rewrite this as inches, divide by 2.5:
The surface area of the cube in square inches is
Example Question #52 : Areas And Perimeters Of Polygons
The volume of a cube is 64 cubic inches. Find the side length of the cube and its surface area.
The volume of a cube is 
A cube has six faces and the surface area of a cube is 
Surface area =
Example Question #2 : How To Find The Area Of A Square
A square has an area of 16 square inches. Give the diagonal of the square.
In order to determine the length of the diagonal of a square we would use the Pythagorean Theorem. First we should find the side length:
Now, "square" the length of one side and multiply by 2, then take the square root of that number to get the length of the diagonal:
Example Question #54 : Areas And Perimeters Of Polygons
John is going to apply a fertilizer to his farm which has a dimension of 200 feet by 200 feet. Every pound of the fertilizer that he is going to use is sufficient for 40 square feet. If the fertilizer costs 2 dollars per pound, how much he should spend to fertilize his farm?
The area of the farm is:
Every pound of the fertilizer costs $2, so he needs to spend 
All SSAT Upper Level Math Resources
