# Rectangle

All figures which have four sides are known as quadrilaterals. The following are the major types of quadrilaterals.

## Rectangle:* *In a rectangle, each pair of opposite sides is parallel and equal. Diagonals are equal and bisect each other, but not at right angles.

Â· Perimeter of rectangle = 2(l+b)

Â· Area of rectangle = l Ã— b

The length and breadth of a rectangle are 40 meters and 20 meters respectively. A 2 meters wide path is made all around it on the outside. Find the area of the path in sq. metres.

Area of the original rectangle = 40 Ã— 20 = 800.

A 2 meter wide path is made around it. Adding the path,

Length of the greater rectangle is 40 + 4 = 44

(add 2 meters on each side)

Breadth of the greater rectangle is 20 + 4 = 24

Area of the greater rectangle = 44 Ã— 24 = 1056.

Difference between these two is the area of path only. As shown in the diagram,

outside margin is the path.

âˆ´ area of the path = 1056 â€“ 800 = 256 sq. metres.

The length of a rectangle is 50 meters and its breadth is 40 metres. A 3 metres wide path is made, inside it, in the middle crossing each other. Find the area of path.

The paths can be treated as two different

rectangles. One with sides 50 Ã— 3 and the other another

is having the side 40 Ã— 3.

The area of one of these rectangles is 50 Ã— 3 = 150

The area of the second rectangle is 40 Ã— 3 = 120

Out of this, a small square of 3 Ã— 3 is there which has been included in both of these rectangles. The area of the path is 120 + 150 â€“ 9 = 261 sq. mts.

# Square

**In a square, **

- All the four sides are equal
- All the four angles are equal and each angle is equal to 90Â°
- Diagonals are equal and bisect each other at right angles.
- Perimeter = 4a
- Area = a
^{2} - Diagonal = aâˆš2
- Area of a square is also equal to = Â½ (diagonal)
^{2}

^{ }

# Rhombus

In a rhombus,

All the four sides are equal.

All the angles are not equal.

Diagonals are not equal but they bisect each other at right angles.

Area = Â½ Ã— d_{1} Ã— d_{2 }where d_{1} and d_{2} are two diagonals of a rhombus.

# Parallelogram

- Area of Parallelogram = Base Ã— Height.
- Each diagonal of a parallelogram, divides it into two triangles of equal area.

# Trapezium

In a trapezium, one pair of opposite sides is parallel and equal. If the opposite sides are â€˜aâ€™ and â€˜bâ€™ and distance between them is â€˜câ€™. Then the area of this trapezium is as follows

= Â½ (a + b) Ã— c