HSPT Math : Concepts
Study concepts, example questions & explanations for HSPT Math
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Example Questions
Example Question #6 : Geometry
Give the area of the above triangle.
By Heron's formula, the area of a triangle given its sidelengths is
where 
or half the perimeter.
Setting 
Therefore,
Example Question #1 : How To Find The Area Of A Parallelogram
Find the area of the following parallelogram:
Note: The formula for the area of a parallelogram is 
The base of the parallelogram is 10, while the height is 5.
Example Question #1 : Parallelograms
Find the area:
The area of a parallelogram can be determined using the following equation:
Therefore,
Example Question #1 : How To Find The Area Of A Rectangle
What is the area of a rectangle with length 
The formula for the area, 
To calculate this area, just multiply the two terms.
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 #31 : Rectangles
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 #1191 : Concepts
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.
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