Q17.

Find the area of each figure:

A rhombus with perimeter and one diagonal 30 .

Verified

Answer

The area of given figure is 240 square units.

1Step 1. Given information.

Perimeter $p = 68$ and one diagonal $d_{1} = 30$ .

2Step 2. Analyze the given information.

As the all four sides are equal in length in rhombus.

Let common side be a and Perimeter is 68 ,

Then, we can say $a + a + a + a = 68$

$4 a = 68$

$a = 17$

3Step 3. Find the other diagonal of rhombus.

We can use Pythagoras theorem.

Pythagorean Theorem define that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of other sides.

$17^{2} = 15^{2} + x^{2}$

$x^{2} = 289 - 225$

$x^{2} = 64$

$x = 8$

So the other diagonal will be $8 + 8 = 16$

4Step 4. Find the area of given figure.

Area of rhombus can be found using the formula

$A = \frac{1}{2} d_{1} d_{2}$

Where,

$d_{1}$ and $d_{2}$ are the diagonals of a rhombus

$A = \frac{1}{2} d_{1} d_{2}$

$= \frac{1}{2} \times 30 \times 16$

$= 30 \times 8$

= 240 Square units.

Therefore, the area of given figure is240 square units.