Chapter 11, Problem 19RP

Solution

To Calculate: The area of a rhombus.

The area of a rhombus is $120$ unit ${}^2$

Given information:

Perimeter of rhombus = $52$

Longer diagonal = $24$

Formula used:

Here, we are using the formula:

Area of a rhombus with perimeter and a diagonal = $\frac{1}{4}a\sqrt{P^2-4a^2}$

(Where, “ a ” is diagonal, “ P ” is perimeter)

Calculation:

Here, area of a rhombus with perimeter and a diagonal = $\frac{1}{4}a\sqrt{P^2-4a^2}$

(Where “ a ” is $24$ and “ P ” is $52$ )

Now, putting these values in the above formula:

➔$\frac{1}{4}\times 24\sqrt{{\left(24\right)}^2-4\times {\left(24\right)}^2}$

➔$6\sqrt{2704-2304}$

➔$6\sqrt{400}$

➔$6\times 20=120$

Conclusion: Hence, the area of a rhombus is $120$ unit ${}^2$