**Area of Square Worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on area of square.

Before look at the worksheet, if you wish to learn the stuff area of square,

**Problem 1 :**

Find the area of the square having side length 24 cm.

**Problem 2 :**

If the area of a square is 64 square inches, then find the length of each side.

**Problem 3 :**

Find the area of the figure shown below.

**Problem 4 :**

The square has side length of 250 cm. Find its area in square meter.

**Problem 5 :**

If the length of each diagonal is 2√2 cm, then find its area.

**Problem 6 :**

If the perimeter of a square is 30 inches, then find its area.

**Problem 7 :**

Find the area of the figure which has the following vertices in xy-coordinate plane.

E(-1, 3), F(4, 3), G(4, -2) and H(-1, -2)

**Problem 8 :**

PQ is one of the sides of the square PQRS and the side PQ is defined by P(0, 2) and C(6, 9). Find the area of the square PQRS.

**Problem 9 :**

AC is one of the diagonals of the square ABCD and the diagonal AC is defined by A(1, 4) and C(4, 8). Find the area of the square ABCD.

**Problem 10 :**

If the lengths of the diagonals of two squares are in the ratio 2 : 5. then find the ratio of their areas.

**Problem 1 :**

Find the area of the square having side length 24 cm.

**Solution:**

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

= s^{2 }

Substitute 24 for s.

= 24^{2}

= 576

So, the area of the square is 576 square cm.

**Problem 2 :**

If the area of a square is 64 square inches, then find the length of each side.

**Solution:**

Area of the square = 64 in^{2}

s^{2} = 64

Find positive square root on both sides.

√s^{2} = √(8 ⋅ 8)

s = 8

So, the length of each side of the square is 8 inches.

**Problem 3 :**

Find the area of the figure shown below.

**Solution : **

The figure shown above is a four sided closed figure. The lengths of all the four sides are equal and each vertex angle is right angle or 90^{o}.

Therefore, the figure shown above is a square with side length 15 units.

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

= s^{2 }

Substitute 15 for s.

= 15^{2}

= 225

So, the area of the figure shown below is 225 square units.

**Problem 4 :**

The square has side length of 250 cm. Find its area in square meter.

**Solution:**

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

= s^{2 }

Substitute 250 for s.

= 250^{2}

= 62500 cm^{2} -----(1)

We know

100 cm = 1 m

Square both sides.

(100 cm)^{2} = (1 m)^{2}

100^{2} cm^{2} = 1^{2} m^{2}

10000 cm^{2} = 1 m^{2}

Therefore, to convert centimeter square into meter square, we have to divide by 10000.

(1)-----> Area of the square = 62500 cm^{2}

Divide the right side by 10000 to convert cm^{2} into m^{2}.

Area of the square = (62500 / 10000) m^{2}

= 6.25 m^{2}

So, the area of the square is 6.25 square meter.

**Problem 5 :**

If the length of each diagonal is 2√2 cm, then find its area.

**Solution:**

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

= 1/2 ⋅ d^{2}

Substitute 2√2 for d.

= 1/2 ⋅ (2√2)^{2}

Simplify.

= 1/2 ⋅ (4 ⋅ 2)

= 1/2 ⋅ (8)

= 4

So, the area of the square is 4 square cm.

**Problem 6 :**

If the perimeter of a square is 30 inches, then find its area.

**Solution:**

Perimeter = 30 icnhes

4s = 30

Divide each side by 4.

s = 7.5

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

= s^{2}

Substitute 7.5 for s.

= 7.5^{2}

= 56.25

So, the area of the square is 56.25 square inches.

**Problem 7 :**

Find the area of the figure which has the following vertices in xy-coordinate plane.

E(-1, 3), F(4, 3), G(4, -2) and H(-1, -2)

**Solution:**

Draw a sketch with the given vertices.

Clearly, the above figure is a square with side length of 5 units.

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

= s^{2}

Substitute 5 for s.

= 5^{2}

= 25

So, the area of the square is 25 square units.

**Problem 8 :**

PQ is one of the sides of the square PQRS and the side PQ is defined by P(0, 2) and C(6, 9). Find the area of the square PQRS.

**Solution:**

**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 Q, substitute **

**(x _{1}, y_{1}) = (0, 2)**

**(x _{2}, y_{2}) = (6, 9)**

**in the above formula.**

**Distance between P and Q : **

**= √[(6-0) ^{2 }+ (9-2)^{2}]**

**= √[6 ^{2 }+ 7^{2}]**

**= ****√[36 ^{ }+ 49]**

**= ****√85**

**Therefore, the length of the side PQ is ****√85**** units.**

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

= s^{2}

Substitute s = **√8**5.

= (**√8**5)^{2}

= 85

So, the area of the square PQRS is 85 square units.

**Problem 9 :**

AC is one of the diagonals of the square ABCD and the diagonal AC is defined by A(1, 4) and C(4, 8). Find the area of the square ABCD.

**Solution:**

**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 C, substitute **

**(x _{1}, y_{1}) = (1, 4)**

**(x _{2}, y_{2}) = (4, 8)**

**in the above formula.**

**Distance between A and C : **

**= √[(4-1) ^{2 }+ (8-4)^{2}]**

**= √[3 ^{2 }+ 4^{2}]**

**= ****√[9 ^{ }+ 16]**

**= ****√25**

**= 5**

**Therefore, the length of the diagonal AC 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 ABCD is 12.5 square units.

**Problem 10 :**

If the lengths of the diagonals of two squares are in the ratio 2 : 5. then find the ratio of their areas.

**Solution:**

From the ratio 2 : 5, let the diagonals of two squares be 2x and 5x respectively.

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

= 1/2 ⋅ d^{2}

= 1/2 ⋅ (2x) = 1/2 ⋅ (4x = 4x |
= 1/2 ⋅ (5x) = 1/2 ⋅ (25x = 25x |

Ratio of the areas :

= (4x^{2} / 2) : (25x^{2} / 2)

Multiply each term of the ratio by 2.

= 4x^{2} : 25x^{2}

Divide each term by x^{2}.

= 4 : 25

So, the ratio of the areas of two squares is 4 : 25.

After having gone through the stuff given above, we hope that the students would have understood, "Area of Square Worksheet".

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