HSPT Math : Geometry
Study concepts, example questions & explanations for HSPT Math
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Example Questions
Example Question #5 : Area Of A Triangle
What is the area of the triangle?
Area of a triangle can be determined using the equation:
Example Question #1 : Area Of A Triangle
Bill paints a triangle on his wall that has a base parallel to the ground that runs from one end of the wall to the other. If the base of the wall is 8 feet, and the triangle covers 40 square feet of wall, what is the height of the triangle?
In order to find the area of a triangle, we multiply the base by the height, and then divide by 2.
In this problem we are given the base and the area, which allows us to write an equation using 
Multiply both sides by two, which allows us to eliminate the two from the left side of our fraction.
The left-hand side simplifies to:
The right-hand side simplifies to:
Now our equation can be rewritten as:
Next we divide by 8 on both sides to isolate the variable:
Therefore, the height of the triangle is 
Example Question #41 : Geometry
The hypotenuse of a right triangle is 25 inches; it has one leg 15 inches long. Give its area in square feet.
The area of a right triangle is half the product of the lengths of its legs, so we need to use the Pythagorean Theorem to find the length of the other leg. Set 
The legs are 15 and 20 inches long. Divide both dimensions by 12 to convert from inches to feet:
Now find half their product:
Example Question #1 : How To Find The Area Of A Square
What is the area of a square with perimeter 64 inches?
It cannot be determined from the information given.
The perimeter of a square is four times its sidelength, so a square with perimeter 64 inches has sides with length 16 inches. Use the area formula:
Example Question #41 : Geometry
The area of the square is 81. What is the sum of the lengths of three sides of the square?
A square that has an area of 81 has sides that are the square root of 81 (side2 = area for a square). Thus each of the four sides is 9. The sum of three of these sides is 
Example Question #41 : Geometry
The length of one side of a square is 
The area of any quadrilateral is found by multiplying the length by the width. Because a square has four equal sides, the length and width are the same. For the square in this question, the length and width are 
Remember: area is always given in units2 .
Example Question #41 : Geometry
If a square has a side that is 3 yards long, what is the area in square feet?
The area of a square is found by multiplying the length of a side by itself.
If one side is 3 yards, this means one side is 9 feet since there are 3 feet in a yard.
Since every side is of equal length, you would multiply 9 feet by 9 feet to find the area.
This results in 81 square feet, which is the correct answer.
Example Question #1 : How To Find The Perimeter Of A Trapezoid
Find the perimeter of the trapezoid:
The perimeter of any shape is equal to the sum of the lengths of its sides:
Example Question #47 : Geometry
The perimeter of a square is 
A square has four equal sides. Given the value of the perimeter, divide the perimeter by four to determine each side length.
Square the side length to find the area since the area of the square is 
Example Question #41 : Geometry
Find the area of a square in 
Write the area for a square.
Convert 
Substitute the side.
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