**Area of squares and rectangles :**

Area of squares and rectangles is the basic topic in mensuration.

A plane figure with four equal straight sides and four right angles is called square. |

**Area of square :**

Generally there are 3 ways to find area of a square. We have to use one of those ways according to the information given in the question.

Area of the square = a²

Here "a" stands for the length of each side.

Area of the square = d²/2

here "d" stands for length of diagonal.

Side length of square = (1/4) x perimeter of square

A plane figure with four straight sides and four right angles.In which the opposite sides are having the same length. |

**Area of rectangles :**

Area of rectangle = L x W

Here "L" represents length of the rectangle and "W" represents the width of the rectangle.

**Example 1 :**

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

**Solution :**

Area of the square = a² = 24²

= 24 x 24

= 576 cm²

Hence, area of square is 576 cm²

**Example 2 :**

A square is of area 64 cm². Then find its side length.

**Solution :**

Area of the square = 64 cm²

a² = 64 cm²

a = √64

= √8 x 8 ==> 8 cm

Hence, side length of square is 8 cm

**Example 3 :**

The diagonals of two squares are in the ratio 2:5. Find the ratio of their area.

**Solution :**

Let the diagonals of two squares be 2x and 5x respectively.

Area of a square when diagonal is given = (1/2) x d²

Area of first square = (1/2) **x **(2x)²

= (1/2) **x ** 4x² ==> 2x²

Area of second square = (1/2) **x **(5x)²

= (1/2) **x ** 25x² ==> 25x² / 2

Ratio of their areas ==> 2x² : (25x² / 2)

= 4 : 25

**Example 4 :**

The length and width of the rectangle are in the ratio 5:2 .If the area of the rectangle is measuring 147 cm². Then find the length and width of the rectangle.

**Solution :**

5x and 2x be the length and width of the rectangle respectively.

Area of the rectangle = 147 cm²

Length x width = 147

5x **x** 2x = 147

7x² = 147

x² = 147/7

x² = 21

x = √21

Length = 5x = 5√21 cm

Width = 2x = 2√21 cm

**Example 5 :**

Find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of $12.40 per square meter.

**Solution :**

From the given information we come to know that

Area of carpet = Area of room ---- (1)

area of rectangle = length x width

0.75 x width of carpet = 13 x 9

width of carpet = (13 x 9) /0.75

= 117/0.75

= 156 m

Cost of carpeting = 156 x 12.40 = $ 1934.40

- Area and polygons
- Inverse operations
- Area of square and rectangles
- Area of quadrilaterals
- Area of a parallelogram
- Finding the area of a trapezoid
- Finding the area of a rhombus
- Area of triangles
- Finding the area of a triangle
- Problems using area of a triangles
- Solving area equations
- Writing equations using the area of a trapezoid
- Solving multistep problems
- Area of polygons
- Finding areas of polygons
- Real world problems involving area and perimeter of polygon

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