**Definition of Rectangle:**

Rectangle is a quadrilateral which has equal opposite sides and all angles are right angles, not all sides are equal only the pair of opposite sides are equal.

Rectangles are a parallelogram in which adjacent sides are perpendicular to each other i.e every angle is equal to 90^{0}.

A square is a special case of rectangles which has all four sides are equal to each other.

**Properties of rectangles:-**

- Rectangles are cyclic.
- Rectangles are equiangular.
- Rectangles are vertex transitive.
- The diagonals are bisecting each other.
- The diagonals are equal to each other.

Area of Rectangle = Length(l) * Breadth(w)

Perimeter of Rectangle = 2(Length+Breadth)

Length of diagonals = √ (l^{2} + w^{2})

A rectangle has circum-circle with circum-radius R = ½√ (l^{2} + w^{2})

**Example:**

**Question:** Find the area and perimeter of a rectangle that’s side measures as 5cm and 8cm.

**Solution:**

Area of Rectangle = Length * Breadth

= 5*8

= 40 cm^{2}

Perimeter of Rectangle = 2(Length+Breadth)

= 2(5+8)

= 26 cm

**Questions1:** Find the area and perimeter of a rectangle that’s side measures as 6cm and 8cm. and also find the length of diagonal.

**Solution:**

Area of Rectangle = Length * Breadth

= 6*8

= 48 cm^{2}

Perimeter of Rectangle = 2(Length+Breadth)

= 2(6+8)

= 28 cm

Length of diagonals = √ (l^{2} + w^{2})

= √(36+64)

= 10 cm

**Questions2:**Find the measure of length and breadth of a rectangle that’s area is 84 cm^{2} and Perimeter is given as 38 cm.

**Solution:**

Area of Rectangle = Length * Breadth

84 = l*b ------- (i)

38 = 2(l+b)

19 = l+b

19-b = l

from (i)

84 = b*(19-b)

84 = 19b-b^{2}

b^{2} -19b+84 = 0

So, b = 7cm and l = 12 cm.

**Questions3:** Find the circumradius of a rectangle which has cicumcircle with sides 6 cm and 8 cm.

**Solution:**

R = ½√ (l^{2} +w^{2})

=½√(36+64)

=5 cm

**Questions 4:** find the circumradius of a rectangle, the sum of square of sides is given as 36 cm.

**Solution:**

R = ½√ (a^{2} + b^{2})

Here (a^{2} + b^{2}) = 36

R = ½√36

R = 3 cm