PSAT Math : How to find the area of a square
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Example Questions
Example Question #1 :Squares
一个BCD and EFGH are squares such that the perimeter of ABCD is 3 times that of EFGH. If the area of EFGH is 25, what is the area of ABCD?
75
225
15
25
5
225
一个ssign variables such that
One side of ABCD = a
and One side of EFGH = e
Note that all sides are the same in a square. Since the perimeter is the sum of all sides, according to the question:
4a = 3 x 4e = 12e or a = 3e
From that area of EFGH is 25,
e x e = 25 so e = 5
Substitute a = 3e so a = 15
We aren’t done. Since we were asked for the area of ABCD, this is a x a = 225.
Example Question #1 :Squares
一个square has an area of 36. If all sides are doubled in value, what is the new area?
144
48
72
132
108
144
Let S be the original side length. S*S would represent the original area. Doubling the side length would give you 2S*2S, simplifying to 4*(S*S), giving a new area of 4x the original, or 144.
Example Question #8 :Squares
If the perimeter of a square is equal to twice its area, what is the length of one of its sides?
一个rea of a square in terms of each of its sides:
一个rea = S x S
Perimeter of a square:
Perimeter = 4S
So if 'the perimeter of a square is equal to twice its area':
2 x Area = Perimeter
2 x [S x S] = [4S]; divide by 2:
S x S = 2S; divide by S:
S = 2
Example Question #9 :Squares
Freddie is building a square pen for his pig. He plans to buyxfeet of fencing to build the pen. This will result in a pen with an area ofpsquare feet. Unfortunately, he only has enough money to buy one third of the planned amount of fencing. Which expression represents the area of the pen he can build with this limited amount of fencing?
3p
p/6
p/3
p/9
9p
p/9
If Freddie usesxfeet of fencing makes a square, each side must bex/ 4英尺长。这个正方形的面积是(x/4)2=x2/16 =psquare feet.
If Freddie uses one third ofxfeet of fencing makes a square, each side must bex/12 feet long. The area of this square is (x/12)2=x2/144 = 1/9(x2/16) = 1/9(p) =p/9 square feet.
一个lternate method:
The scale factor between the small perimeter and the larger perimeter = 1 : 3. Since we're comparing area, a two-dimensional measurement, we can square the scale factor and see that the ratio of the areas is 12: 32= 1 : 9.
Example Question #1 :How To Find The Area Of A Square
If the diagonal of a square measures
This is an isosceles right triangle, so the diagonal must equal
Example Question #41 :Quadrilaterals
一个square
The area of
Example Question #3 :How To Find The Area Of A Square
The perimeter of a square is
The perimeter of a square is given by
So the area of the new square is given by
Example Question #1 :How To Find The Area Of A Square
一个half circle has an area of
108
36
81
144
72
144
If the area of the half circle is
Use the formula for the area of a circle to solve for the radius:
36π = πr2
r = 6
If the radius is 6, then the diameter is 12. We know that the sides of the square are the same length as the diameter, so each side has length 12.
Therefore the area of the square is 12 x 12 = 144.
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