Question

find the area of a rhombus whose side is 15cm while one of the diagonal I'd 24cm long ​

Answer 1

Answer:

The area of the rhombus is 216 sq. cm

Step-by-step explanation:

Consider the rhombus ABCD. The diagonals AC and DB intersect each other at O. The length of diagonal AC is 24 cm. As the diagonals of rhombus are perpendicular and bisect each other the length of AO is 12 cm.

Given: Side of rhombus is 15 cm.

Consider the right angle triangle AOB.

Using the Pythagoras theorem determine the length of OB as follows:

$AB^{2}=AO^{2}+OB^{2}\\15^{2}=12^{2}+OB^{2}\\OB=\sqrt{225-144}\\ =9$

Then the length of diagonal BD is:

$BD=2\times OB\\=2\times9\\=18$

The Area of rhombus is the product of the length of the two diagonals divided by 2.

$Area\ of ABCD=\frac{AC\times BD}{2}\\ =\frac{24\times 18}{2} \\=216$

Thus, the area of the rhombus is 216 sq. cm.