Name: Finding area of triangle using base and height
Uploaded: 2019-07-19
Duration: 10 min 43 s
Description: Do you know that you can find the area of a triangle using its base and height? Well, that is what we'll learn about in this informative video. Learn more.

Question

If the perimeter of a rhombus is $68 c m$ and one of its diagonals is $30 c m$ , find its area.

Accepted Answer

We know that the area of the rhombus $= \frac{1}{2} (d_{1}) (d_{2})$ , where $d_{1}$ and $d_{2}$ are the two diagonals of the rhombus.

Here, it is given that the perimeter of the rhombus is $68 cm$ and one of the diagonals $(d_{1})$ is $30 cm .$

Now we have to find the other diagonal $(d_{2})$ .

A rhombus is a quadrilateral which has four equal sides and two diagonals of different lengths.

So, the perimeter of a rhombus $= 4 \times$ length of side.

$\Rightarrow 68 c m = 4 \times$ length of side

$\Rightarrow$ length of side $= \frac{68 cm}{4} = 17 cm$

We consider that the length of a diagonal, say $A C = 30 cm$ is given.

We know that diagonals of a rhombus bisect each other at right-angled.

So, $A O = O C = 15 cm$

Therefore, in $△ A O D,$ applying Pythagoras theorem,

$\begin{array}{rcl} A O^{2} + O D^{2} & = & A D^{2} \end{array}$

$\Rightarrow 15^{2} + O D^{2} = 17^{2}$

$\begin{array}{rcl} \Rightarrow \end{array} O D^{2} = 289 - 225 = 64$

$\Rightarrow O D = 8 c m$

Therefore, other diagonal, $d_{2} = 2 \times O D = 2 \times 8 m = 16 cm$

Hence, the area of rhombus $= \frac{1}{2} (30) (16) = 240 s q . c m$

If the perimeter of a rhombus is $68 c m$ and one of its diagonals is $30 c m$ , find its area.

Important Questions on Mensuration

Learn and Prepare for any exam you want !

If the perimeter of a rhombus is 68 cm and one of its diagonals is 30 cm, find its area.

Important Questions on Mensuration

Learn and Prepare for any exam you want !

If the perimeter of a rhombus is $68 c m$ and one of its diagonals is $30 c m$ , find its area.