All PSAT Math Resources
Example Question #1 : How To Find The Area Of A Rectangle
A contractor is going to re-tile a rectangular section of the kitchen floor. If the floor is 6ft x 3ft, and he is going to use square tiles with a side of 9in. How many tiles will be needed?
We have to be careful of our units. The floor is given in feet and the tile in inches. Since the floor is 6ft x 3ft. we can say it is 72in x 36in, because 12 inches equals 1 foot. If the tiles are 9in x 9in we can fit 8 tiles along the length and 4 tiles along the width. To find the total number of tiles we multiply 8 x 4 = 32. Alternately we could find the area of the floor (72 x 36, and divide by the area of the tile 9 x 9)
Example Question #41 : Quadrilaterals
The rectangular bathroom floor in Michael’s house is ten feet by twelve feet. He wants to purchase square tiles that are four inches long and four inches wide to cover the bathroom floor. If each square tile costs $2.50, how much money will Michael need to spend in order to purchase enough tiles to cover his entire bathroom floor?
The dimensions for the bathroom are given in feet, but the dimensions of the tiles are given in inches; therefore, we need to convert the dimensions of the bathroom from feet to inches, because we can’t compare measurements easily unless we are using the same type of units.
Because there are twelve inches in a foot, we need to multiply the number of feet by twelve to convert from feet to inches.
10 feet = 10 x 12 inches = 120 inches
12 feet = 12 x 12 inches = 144 inches
This means that the bathroom floor is 120 inches by 144 inches. The area of Michael’s bathroom is therefore 120 x 144 in2 = 17280 in2.
Now, we need to find the area of the tiles in square inches and calculate how many tiles it would take to cover 17280 in2.
Each tile is 4 in by 4 in, so the area of each tile is 4 x 4 in2, or 16 in2.
If there are 17280 in2 to be covered, and each tile is 16 in2, then the number of tiles we need is 17280 ÷ 16, which is 1080 tiles.
The question ultimately asks us for the cost of all these tiles; therefore, we need to multiply 1080 by 2.50, which is the price of each tile.
The total cost = 1080 x 2.50 dollars = 2700 dollars.
The answer is $2700.
Example Question #2 : How To Find The Area Of A Rectangle
Ron has a fixed length of wire that he uses to make a lot. On Monday, he uses the wire to make a rectangular lot. On Tuesday, he uses the same length of wire to form a square-shaped lot. Ron notices that the square lot has slightly more area, and he determines that the difference between the areas of the two lots is sixteen square units. What is the positive difference, in units, between the length and the width of the lot on Monday?
Let’s say that the rectangular lot on Monday has a length of l and a width of w. The area of a rectangular is the product of the length and the width, so we can write the area of the lot on Monday as lw.
Next, we need to find an expression for the area of the lot on Tuesday. We are told that the lot is in the shape of a square and that it uses the same length of wire. If the length of the wire used is the same on both days, then the perimeter will have to remain the same. In other words, the perimeter of the square will equal the perimeter of the rectangle. The perimeter of a rectangle is given by 2l + 2w.
We also know that if s is the length of a side of a square, then the perimeter is 4s, because each side of the square is congruent. Let’s write an equation that sets the perimeter of the rectangle and the square equal.
2l + 2w = 4s
If we divide both sides by 4 and then simplify the expression, then we can write the length of the square as follows:
Example Question #203 : Plane Geometry
A rectangle has a width of 2x. If the length is five more than 150% of the width, what is the area of the rectangle?
10(x + 1)
6x2 + 10x
5x + 10
6x2 + 5
5x + 5
6x2 + 10x
Given that w = 2x and l = 1.5w + 5, a substitution will show that l = 1.5(2x) + 5 = 3x + 5.
A = lw = (3x + 5)(2x) = 6x2 + 10x
Example Question #3 : How To Find The Area Of A Rectangle
Rectangle ABCD is shown in the figure above. Points A and B lie on the graph of y = 64 – x2 , and points C and D lie on the graph of y = x2 – 36. Segments AD and BC are both parallel to the y-axis. The x-coordinates of points A and B are equal to –k and k, respectively. If the value of k changes from 2 to 4, by how much will the area of rectangle ABCD increase?
Example Question #4 : How To Find The Area Of A Rectangle
George wants to paint the walls in his room blue. The ceilings are 10 ft tall and a carpet 12 ft by 15 ft covers the floor. One gallon of paint covers 400 and costs $40. One quart of paint covers 100 and costs $15. How much money will he spend on the blue paint?
The area of the walls is given by
One gallon of paint covers 400 and the remaining 140 would be covered by two quarts.
So one gallon and two quarts of paint would cost
Example Question #5 : How To Find The Area Of A Rectangle
Daisy gets new carpet for her rectangluar room. Her floor is . The carpet sells for $5 per square yard. How much did she spend on her carpet?
Since the room measurements are 7 yards by 8 yards. The area of the floor is thus 56 square yards. It would cost .
Example Question #337 : Plane Geometry
The length of a rectangular rug is five more than twice its width. The perimeter of the rug is 40 ft. What is the area of the rug?
For a rectangle, and where is the width and is the length.
Let and .
So the equation to solve becomes or .
Thus and , so the area is .
Example Question #6 : How To Find The Area Of A Rectangle
The front façade of a building is 100 feet tall and 40 feet wide. There are eight floors in the building, and each floor has four glass windows that are 8 feet wide and 6 feet tall along the front façade. What is the total area of the glass in the façade?
Glass Area per Window = 8 ft x 6 ft = 48 ft2
Total Number of Windows = Windows per Floor * Number of Floors = 4 * 8 = 32 windows
Total Area of Glass = Area per Window * Total Number of Windows = 48 * 32 = 1536 ft2
Example Question #46 : Quadrilaterals
Note: Figure NOT drawn to scale
What percent of Rectangle is pink?
The pink region is Rectangle . Its length and width are
so its area is the product of these, or
The length and width of Rectangle are
so its area is the product of these, or
We want to know what percent 117 is of 240, which can be answered as follows: