SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)
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All SSAT Middle Level Math Resources
Example Questions
Example Question #1 : Geometry
Find the slope of the line that passes through the points 
Cannot be determined
Using the slope formula, where 
Example Question #3 : Coordinate Geometry
Find the slope of a line with points 
Cannot be determined
Using the slope formula, where 
Example Question #4 : How To Find A Line On A Coordinate Plane
Billy set up a ramp for his toy cars. He did this by taking a wooden plank and putting one end on top of a brick that was 3 inches high. He then put the other end on top of a box that was 9 inches high. The bricks were 18 inches apart. What is the slope of the plank?
The value of the slope (m) is rise over run, and can be calculated with the formula below:
The coordinates of the first end of the plank would be (0,3), given that this is the starting point of the plank (so x would be 0), and y would be 3 since the brick is 3 inches tall.
The coordinates of the second end of the plank would be (18,9) since the plank is 18 inches long (so x would be 18) and y would be 9 since the box was 9 inches tall at the other end.
From this information we know that we can assign the following coordinates for the equation:
Below is the solution we would get from plugging this information into the equation for slope:
This reduces to
Example Question #1 : How To Find A Triangle On A Coordinate Plane
Find the area of the above triangle, given that it has a height of 12 and a base of 10.
Because this is a right triangle, the area formula is simply:
Thus, the solution is:
Example Question #2 : How To Find A Triangle On A Coordinate Plane
Given the above triangle is an equilateral triangle, find the perimeter in units as drawn in the coordinate system.
Using the coordinate system, one can see the base of the triangle is 6 units in length. Since it is an equilateral triangle, the other two sides must also be 6 units each in length. Therefore the perimeter is:
Example Question #1 : How To Find A Triangle On A Coordinate Plane
The isosceles triangle shown above has a perimeter of 22 and base of 6. Find the lengths of the left and right sides, respectively. Assume no other side has a length of 6.
With a perimeter of 22 and base of 6, this means the other two sides must add up to:
Because an isosceles triangle must have two sides equal in length and we know from the problem that no other side equals 6, the two remaining sides must be equal to each other.
Thus, to be equal to each other and also add up to 16, each side must be 8 units in length.
Example Question #2 : How To Find A Triangle On A Coordinate Plane
Given the above triangle has a base of 5 and height of 6, what is the perimeter of the triangle?
First, use the Pythagorean Theorem to find the length of the hypotenuse:
Thus,
Finally, the perimeter is the sum of the sides of the triangle or:
Example Question #191 : Ssat Middle Level Quantitative (Math)
Given triangle 
To find the area of this triangle, we first need to determine the length of sides AB and BC. First, point B shares the same x-coordinate as point A and the same y-coordinate as point C. Thus, B must be located at point (-2,-2).
The length of side AB must then be:
and the length of side BC:
Using the area formula,
we can find the area using the base (side BC) and height (side AB):
Example Question #3 : How To Find A Triangle On A Coordinate Plane
Given triangle 
Use the Pythagorean Theorem to find the length of side AC:
Then, the perimeter is simply the sum of all three sides:
Example Question #192 : Ssat Middle Level Quantitative (Math)
The above triangle has base 6 and height 4. Find the perimeter.
Because the y-axis bisects the base, we can divide the triangle into two, equal right triangles. The base of the right triangle is thus half that of the larger triangle, or 3. The height is still 4. To find the hypotenuse, use the Pythagorean Theorem:
Thus, we now know the base as given in the problem and each of the other two sides (which are also the hypotenuses of the right triangles).
Therefore, the perimeter is:
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All SSAT Middle Level Math Resources
