ACT Math : Plane Geometry
Study concepts, example questions & explanations for ACT Math
All ACT Math Resources
Example Questions
Example Question #2 : Rectangles
If Mrs. Stietz has a patio that measures 96 inches by 72 inches and she wants to cover it with stone tiles that measure one foot by half a foot, what is the minimum number of tiles she needs to cover the patio?
96
48
14
12
6912
96
96. Converting the dimensions of the tiles to inches, they each measure 12 inches by 6 inches. This means that there need to be 8 tiles to span the length of the patio, and 6 tiles to span the width of the patio. She needs to cover the entire area, so we can multiply 8 times 12 to get 96, the number of tiles she needs for the patio.
Example Question #41 : Rectangles
Mark is making a plan to build a rectangular garden. He has 160 feet of fence to form the outside border of the garden. He wants the dimensions to look like the plan outlined below:
What is the area of the garden, rounded to the nearest square foot?
Perimeter: Sum of the sides:
4x + 4x + 2x+8 +2x+8 = 160
12x + 6 = 160
12x = 154
x =
Therefore, the short side of the rectangle is going to be:
And the long side is going to be:
The area of the rectangle is going to be as follows:
Area = lw
Example Question #5 : Rectangles
The area of a rectangle is 
Based on the information given to you, you know that the area could be written as:
Likewise, you know that the perimeter is:
Now, isolate one of the values. For example, based on the second equation, you know:
Dividing everything by 
Now, substitute this into the first equation:
To solve for 
or:
Now, factor this:
You could also get this answer by testing each of your options to see which one works for both the perimeter and the area.
Example Question #8 : Rectangles
A rectangle having a width twice the length of its height has an area of 
Since the width is twice the height, we know that the general area equation, which is
could be written:
Thus, we know:
This means that 
Example Question #11 : How To Find The Area Of A Rectangle
What is the area in 
Because of complexities that arise with square units, it is best to start a problem like this by changing all of your units into inches from the very beginning. Thus, you know that the yard is 
Thus, the area of the yard is 
Example Question #11 : Rectangles
Find the area of a rectangle whose length is 
To find area, simply multiply length times width. Thus,
Example Question #12 : Rectangles
Find the area of a rectangle whose width is 
To solve, simply multiply width and length. Thus,
Example Question #13 : Rectangles
Find the area of rectangle given width of 5 and length of 8.
To solve, simply use the formula for the area of a rectangle. Thus,
Example Question #73 : Quadrilaterals
Erin is getting ready to plant her tulip garden. She wants to plant two tulips per square foot of garden. If her rectangular garden is enclosed by 24 feet of fencing, and the length of the fence is twice as long as its width, how many tulips will Erin plant?
16
64
48
32
24
64
We know that the following represents the formula for the perimeter of a rectangle:
In this particular case, we are told that the length of the fence is twice as long as the width. We can write this as the following expression:
Use this information to substitute in a variable for the length that matches the variable for width in our perimeter equation.
We also know that the length is two times the width; therefore, we can write the following:
The area of a rectangle is found by using this formula:
The area of the garden is 32 square feet. Erin will plant two tulips per square foot; thus, she will plant 64 tulips.
Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle
A rectangle has a height of 
1. Use Pythagorean Theorem with 
2. Solve for 
This rounds down to 
Certified Tutor
All ACT Math Resources
