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.
1. Answer :
Formula for perimeter of a square :
= 4s^{ }
Substitute 14 for s.
= 4(8.5)
= 34
So, the perimeter of the square is 34 cm.
2. Answer :
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
AB^{2} + BC^{2} = AC^{2}
Substitute.
s^{2} + s^{2} = (2√2)^{2}
Simplify and solve for s.
2s^{2} = 2^{2} ⋅(√2)^{2}
2s^{2} = 4 ⋅(2)
2s^{2} = 8
Divide each side by 2.
s^{2} = 4
Find positive square root on both sides.
√s^{2} = √4
√s^{2} = √(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.
3. Answer :
When the length of a side is given, formula for area of a square :
= s^{2 }
Substitute 24 for s.
= 7.5^{2}
= 56.25
So, area of the square is 56.25 square cm.
4. Answer :
When the length of a side is given, formula for area of a square :
= s^{2}
Substitute 3√5 for s.
= (3√5)^{2}
Simplify.
= 3^{2} ⋅ (√5)^{2}
= 9 ⋅ 5
= 45
So, the area of the square is 45 square cm.
5. Answer :
Area of the square = 32 in^{2}
1/2 ⋅ d^{2} = 32
Multiply each side by 2.
d^{2} = 64
Find positive square root on both sides.
√d^{2} = √(8 ⋅ 8)
d = 8
So, the length of diagonal is 8 inches.
6. Answer :
When the length of a side is given, formula for area of a square :
= s^{2 }
Substitute 12 for s.
= 36^{2}
= 1296 in^{2} -----(1)
We know
12 inches = 1 ft
Square both sides.
(12 inches)^{2} = (1 ft)^{2}
12^{2} in^{2} = 1^{2} ft^{2}
144 in^{2} = 1 ft^{2}
Therefore, to convert square inches into meter square feet, we have to divide by 144.
(1)-----> Area of the square = 1296 in^{2}
Divide the right side by 144 to convert in^{2} into ft^{2}.
Area of the square = 1296/144 ft^{2}
= 9 ft^{2}
So, the area of the square is 9 square feet.
7. Answer :
Formula for perimeter of a square :
= 4s
Perimeter of 1^{st} square = 4(4) = 16 cm |
Perimeter of 2^{nd} 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.
8. Answer :
Formula for area of a square :
= s^{2}
Area of 1^{st} square = 4^{2} = 16 cm^{2} |
Area of 2^{nd} square = 5^{2} = 25 cm^{2} |
Ratio of the areas :
= 16 : 25
So, the ratio of the areas of two squares is 16 : 25.
9. Answer :
Distance between the two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is
= √[(x_{2 }- x_{1})^{2 }+ (y_{2 }- y_{1})^{2}]
To find the distance between A and B, substitute
(x_{1}, y_{1}) = (0, 2)
(x_{2}, y_{2}) = (6, 9)
in the above formula.
Distance between A and B :
= √[(6 - 0)^{2 }+ (9 - 2)^{2}]
= √[6^{2 }+ 7^{2}]
= √[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.
10. Answer :
Distance between the two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is
= √[(x_{2 }- x_{1})^{2 }+ (y_{2 }- y_{1})^{2}]
To find the distance between P and R, substitute
(x_{1}, y_{1}) = (1, 4)
(x_{2}, y_{2}) = (4, 8)
in the above formula.
Distance between P and R :
= √[(4 - 1)^{2 }+ (8 - 4)^{2}]
= √[3^{2 }+ 4^{2}]
= √[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 ⋅ d^{2}
Substitute d = 5.
= 1/2 ⋅ 5^{2}
Simplify.
= 1/2 ⋅ 25
= 12.5
So, the area of the square PQRS is 12.5 square units.
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