PERIMETER AND AREA OF SQUARE WORKSHEET
About "Perimeter and Area of Square Worksheet"
Perimeter and Area of Square Worksheet :
Worksheet given in this section is much useful to the students who would like to practice problems on perimeter and area of square.
Before look at the worksheet, if you would like to learn the stuff perimeter and area of square,
Perimeter and Area of Square Worksheet - Problems
Problem 1 :
If the length of each side of a square is 8.5 cm, then find its perimeter.
Problem 2 :
The length of each diagonal of a square is 2√2 cm. Find its perimeter.
Problem 3 :
If a square has the side length of 7.5 cm, then find its area.
Problem 4 :
The length of each side of a square is 3√5 cm. Find its area.
Problem 5 :
The area of a square is 32 square inches. Find the length of its diagonal.
Problem 6 :
The square has side length 36 inches. Find its area in square feet.
Problem 7 :
The lengths of each side of two squares are 4 cm and 5 cm. Find the ratio of their perimeters.
Problem 8 :
The lengths of each side of two squares are 4 cm and 5 cm. Find the ratio of their areas.
Problem 9 :
AB is one of the sides of the square ABCD and the side AB is defined by A(0, 2) and B(6, 9). Find the perimeter of the square ABCD.
Problem 10 :
PR is one of the diagonals of the square PQRS and the diagonal PQ is defined by P(1, 4) and Q(4, 8). Find the area of the square PQRS.
Perimeter and Area of Square Worksheet - Solutions
Problem 1 :
If the length of each side of a square is 8.5 cm, then find its perimeter.
Solution:
Formula for perimeter of a square :
= 4s
Substitute 14 for s.
= 4(8.5)
= 34
So, the perimeter of the square is 34 cm.
Problem 2 :
The length of each diagonal of a square is 2√2 cm. Find its perimeter.
Solution:
To find the perimeter of a square, first we have to know the length of each side.
Let s be the length of each side of the square.
Draw a sketch.
In the figure shown below, consider the right triangle ABC.
By Pythagorean Theorem, we have
AB2 + BC2 = AC2
Substitute.
s2 + s2 = (2√2)2
Simplify and solve for s.
2s2 = 22 ⋅(√2)2
2s2 = 4 ⋅(2)
2s2 = 8
Divide each side by 2.
s2 = 4
Find positive square root on both sides.
√s2 = √4
√s2 = √(2 ⋅ 2)
s = 2
Formula for perimeter of a square.
Perimeter = 4s
Substitute 2 for s.
= 4(2)
= 8
So, the perimeter of the the square is 8 cm.
Problem 3 :
If a square has the side length of 7.5 cm, then find its area.
Solution:
When the length of a side is given, formula for area of a square :
= s2
Substitute 24 for s.
= (7.5)2
= 56.25
So, area of the square is 56.25 square cm.
Problem 4 :
The length of each side of a square is 3√5 cm. Find its area.
Solution:
When the length of a side is given, formula for area of a square :
= s2
Substitute 3√5 for s.
= (3√5)2
Simplify.
= 32 ⋅ (√5)2
= 9 ⋅ 5
= 45
So, the area of the square is 45 square cm.
Problem 5 :
The area of a square is 32 square inches. Find the length of its diagonal.
Solution:
Area of the square = 32 in2
1/2 ⋅ d2 = 32
Multiply each side by 2.
d2 = 64
Find positive square root on both sides.
√d2 = √(8 ⋅ 8)
d = 8
So, the length of diagonal is 8 inches.
Problem 6 :
The square has side length 36 inches. Find its area in square feet.
Solution:
When the length of a side is given, formula for area of a square :
= s2
Substitute 12 for s.
= 362
= 1296 in2 -----(1)
We know
12 inches = 1 ft
Square both sides.
(12 inches)2 = (1 ft)2
122 in2 = 12 ft2
144 in2 = 1 ft2
Therefore, to convert square inches into meter square feet, we have to divide by 144.
(1)-----> Area of the square = 1296 in2
Divide the right side by 144 to convert in2 into ft2.
Area of the square = (1296 / 144) ft2
= 9 ft2
So, the area of the square is 9 square feet.
Problem 7 :
The lengths of each side of two squares are 4 cm and 5 cm. Find the ratio of their perimeters.
Solution:
Formula for perimeter of a square :
= 4s
|
Perimeter of 1st square = 4(4) = 16 cm |
Perimeter of 2nd square = 4(5) = 20 cm |
Ratio of the perimeters :
= 16 : 20
Divide each term by 4.
= 4 : 5
So, the ratio of the perimeters of two squares is 4 : 5.
Problem 8 :
The lengths of each side of two squares are 4 cm and 5 cm. Find the ratio of their areas.
Solution:
Formula for area of a square :
= s2
|
Area of 1st square = 42 = 16 cm2 |
Area of 2nd square = 52 = 25 cm2 |
Ratio of the areas :
= 16 : 25
So, the ratio of the areas of two squares is 16 : 25.
Problem 9 :
AB is one of the sides of the square ABCD and the side AB is defined by A(0, 2) and B(6, 9). Find the perimeter of the square ABCD.
Solution:
Distance between the two points (x1, y1) and (x2, y2) is
= √[(x2-x1)2+(y2-y1)2]
To find the distance between A and B, substitute
(x1, y1) = (0, 2)
(x2, y2) = (6, 9)
in the above formula.
Distance between A and B :
= √[(6-0)2 + (9-2)2]
= √[62 + 72]
= √[36 + 49]
= √85
Therefore, the length of one of the sides is √85 units.
Formula for perimeter of a square :
= 4s
Substitute s = √85.
= 4√85
Use calculator and simplify.
≈ 36.88
So, the perimeter of the square ABCD is about 36.88 units.
Problem 10 :
PR is one of the diagonals of the square PQRS and the diagonal PQ is defined by P(1, 4) and Q(4, 8). Find the area of the square PQRS.
Solution:
Distance between the two points (x1, y1) and (x2, y2) is
= √[(x2-x1)2+(y2-y1)2]
To find the distance between P and R, substitute
(x1, y1) = (1, 4)
(x2, y2) = (4, 8)
in the above formula.
Distance between P and R :
= √[(4-1)2 + (8-4)2]
= √[32 + 42]
= √[9 + 16]
= √25
= 5
Therefore, the length of the diagonal PR is 5 units.
When the length of a diagonal is given, formula for area of a square :
= 1/2 ⋅ d2
Substitute d = 5.
= 1/2 ⋅ 52
Simplify.
= 1/2 ⋅ 25
= 12.5
So, the area of the square PQRS is 12.5 square units.
After having gone through the stuff given above, we hope that the students would have understood, "Perimeter and Area of Square Worksheet".
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
