ACT Math : Plane Geometry
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Example Questions
Example Question #6 : How To Find The Area Of A Square
Given square 
Assume that the length of each midpoint is 1. This means that the length of each side of the large square is 2, so the area of the larger square is 4 square units.
To find the area of the smaller square, first find the length of each side. Because the length of each midpoint is 1, each side of the smaller square is 
The area then of the smaller square is 2 square units.
Comparing the area of the two squares, the larger square is 2 times larger than the smaller square.
Example Question #11 : How To Find The Area Of A Square
If a completely fenced-in square-shaped yard requires 140 feet of fence, what is the area, in square feet, of the lot?
140
70
1225
4900
35
1225
Since the yard is square in shape, we can divide the perimeter(140ft) by 4, giving us 35ft for each side. We then square 35 to give us the area, 1225 feet.
Example Question #391 : Plane Geometry
The perimeter of a square is 
The perimeter of a square is very easy to calculate. Since all of the sides are the same in length, it is merely:
From this, you can calculate the area merely by squaring the side's value:
Example Question #1 : How To Find The Area Of A Square
What is the area of a square with a side length of 
The area of a square is very easy. You merely need to square the length of any given side. That is, the area is defined as:
For our data, this is:
Example Question #1 : How To Find The Area Of A Square
What is the area of a square with a perimeter of 
Not enough information is given.
For a square all the sides are equal, and there are four sides, so divide the perimeter by 4 to determine the side length.
Next to find the area of a square, square the side length:
Don't forget your units!
Example Question #34 : Squares
Eric has 160 feet of fence for a parking lot he manages. If he is using all of the fencing, what is the area of the lot assuming it is square?
The area of a square is equal to its length times its width, so we need to figure out how long each side of the parking lot is. Since a square has four sides we calculate each side by dividing its perimeter by four.
Each side of the square lot will use 40 feet of fence.
Example Question #6 : How To Find The Area Of A Square
A square garden is inscribed inside a circular cobblestone path. If the radius of the cobblestone path is 
If a square is inscribed inside a circle, the diameter of the circle is the diagonal of the square. Since we know the radius of the circle is 
All squares have congruent sides; thus, the diagonal of a square creates two isosceles right triangles. The ratio of the lengths of the sides of an isosceles right triangle are 
The area of a square is 
Thus, the area of our square garden is
Example Question #161 : Quadrilaterals
Find the area of a square whose side length is 
To find area, simply square the side length. Thus,
Example Question #391 : Geometry
Find the area of a square with side length 5.
To solve, simply use the formula for the area of a square given side length s. Thus,
Example Question #843 : Basic Geometry
A square is circumscribed on a circle with a 6 inch radius. What is the area of the square, in square inches?
48
36
24
144
144
We know that the radius of the circle is also half the length of the side of the square; therefore, we also know that the length of each side of the square is 12 inches.
We need to square this number to find the area of the square.
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