Question

find the area of rhombus having length of side as 13 cm and one of the diagonal as 24cm​

Answer 1

Step-by-step explanation:

Definition :

A Rhombus is a quadrilateral which has equal sides and its diagonal bisects each other at right angles.

$\sf{Area \: of \: rhombus \: = \frac{1}{2} \times digonal_{1} \times \: diagonal_{2}}$

Given :-

Length of one side of Rhombus = 13 cm

Length of the diagonal of Rhombus = 24 cm

See the above attachment for the diagram.

As the diagonals bisects perpendicularly so in right triangle AOB we have,

Hypotenuse (H) = 13 = AB

Base (B) = 12 = OA

Perpendicular (P) = ? = OB

So by Pythagoras formula,

P² + B² = H²

P² + 12² = 13²

P² = 13² - 12²

P² = 25

P = (25)¹/²

P = 5 cm

Therefore other side OB is 5 cm.

Hence the length of diagonal BC is

5 + 5 = 10 cm.

Now area of Rhombus = 1/2*24*10

= 120 cm²

Therefore the area of Rhombus is 120 cm².