Question

find the area of a rhombus having each side equal to 13 CM and one of the diagonals is 24 cm

Answer 1

Find the value of d2 and then find the area

Answer 2

Answer:

Area of the Rhombus is 120 centimeter square.

Step-by-step explanation:

Given : Each side of rhombus is 13 cm and one diagonal is 24 cm.

To find : The area of the Rhombus?

Solution :  

One side rhombus = 13 cm  

Length of one diagonal = 24 cm

Property of rhombus,

Diagonals of rhombus bisect each other at 90 degree.

Now, Taking 1/4 portion of rhombus i.e, triangle.

Base = 12 cm (half of diagonal)

Hypotenuse = 13 cm

Applying Pythagoras theorem,

${h}^{2}={b}^{2}+{p}^{2}\\{13}^{2}={12}^{2}+{p}^{2}\\169=144+{p}^{2}\\{p}^{2}=169-144\\p=\sqrt{25}\\p=5$

So, The other diagonal of Rhombus is 5 cm.

Area of rhombus is  

$A=\frac{1}{2}\times (\text{product of diagonal})\\A=\frac{1}{2}\times (24\times 5)\\A=120cm^2$

Therefore, Area of the Rhombus is 120 centimeter square.