# PERIMETER AND AREA OF SQUARE WORKSHEET

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. Formula for perimeter of a square :

=  4s

Substitute 14 for s.

=  4(8.5)

=  34

So, the perimeter of the square is 34 cm.

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.

When the length of a side is given, formula for area of a square :

=  s

Substitute 24 for s.

=  7.52

=  56.25

So, area of the square is 56.25 square cm.

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.

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.

When the length of a side is given, formula for area of a square :

=  s

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.

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.

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.

Distance between the two points (x1, y1) and (x2, y2) is

=  √[(x- x1)+ (y- 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)+ (9 - 2)2]

=  √[6+ 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.

Distance between the two points (x1, y1) and (x2, y2) is

=  √[(x- x1)+ (y- 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)+ (8 - 4)2]

=  √[3+ 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.

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