AREA OF SQUARE WORKSHEET

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.

1. Answer :

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

= s²

Substitute 24 for s.

= 24²

= 576

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

2. Answer :

Area of the square = 64 in²

s² = 64

Find positive square root on both sides.

 √s² = √(8 ⋅ 8)

  s = 8

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

3. Answer :

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 :

= s²

Substitute 15 for s.

= 15²

= 225

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

4. Answer :

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

=  s²

Substitute 250 for s.

= 250²

= 62500 cm² ----(1)

We know

100 cm = 1 m

Square both sides.

(100 cm)² = (1 m)²

100² cm² = 1² m²

10000 cm² = 1 m²

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

(1)----> Area of the square = 62500 cm²

Divide the right side by 10000 to convert cm² into m².

Area of the square = (62500/10000) m²

= 6.25 m²

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

5. Answer :

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

= 1/2 ⋅ d²

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.

6. Answer :

Perimeter = 30 inches

4s = 30

Divide each side by 4.

s = 7.5

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

= s²

Substitute 7.5 for s.

= 7.5²

= 56.25

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

7. Answer :

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

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 :

= s²

Substitute 5 for s.

= 5²

= 25

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

8. Answer :

P(0, 2) and C(6, 9)

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

= √[(x₂ - x₁)²+(y₂ - y₁)²]

To find the distance between P and Q, substitute

(x₁, y₁) = (0, 2)

(x₂, y₂) = (6, 9)

in the above formula.

Distance between P and Q :

= √[(6-0)² + (9-2)²]

= √[6² + 7²]

= √[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 :

= s²

Substitute s = √85.

= (√85)²

= 85

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

9. Answer :

A(1, 4) and C(4, 8)

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

= √[(x₂ - x₁)²+(y₂ - y₁)²]

To find the distance between A and C, substitute

(x₁, y₁) = (1, 4)

(x₂, y₂) = (4, 8)

in the above formula.

Distance between A and C :

= √[(4-1)² + (8-4)²]

= √[3² + 4²]

= √[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 ⋅ d²

Substitute d = 5.

= 1/2 ⋅ 5²

Simplify.

= 1/2 ⋅ 25

= 12.5

So, the area of the square ABCD is 12.5 square units.

10. Answer :

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 ⋅ d²

Ratio of the areas :

= (4x²/2) : (25x²/2)

Multiply each term of the ratio by 2.

= 4x² : 25x²

Divide each term by x².

= 4 : 25

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

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