Question

Find the area of each figure:

A rhombus with perimeter and one diagonal 30 .

Short answer

The area of given figure is 240 square units.

Step-by-step solution

Step 1. Given information.

Perimeter$p=68$ and one diagonal $d_1=30$.

Step 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$a+a+a+a=68$

$4a=68$

$a=17$

Step 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 $8+8=16$

Step 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 arhombus

$A=\frac{1}{2}{d}_1{d}_2$

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

$=30\times 8$

= 240 Square units.

Therefore, the area of given figure is240 square units.