Question

Find the area of a rhombus whose one side measures 5cm and diagonal as 8cm

Answer 1

Use heron's formula to find the areas of triangles and then add it.

Answer 2

Area of a rhombus is 24 $cm^2$.

Step-by-step explanation:

Given:

Let ABCD be the given rhombus with diagonals AC and BD which intersect each other at O such that AC = 8 cm.

Since diagonals of a rhombus bisect each other, we get

$AO=OC=\frac{1}{2} AC=\frac{1}{2} \times 8=4 cm$

Let BO = x and AB = 5 cm   (given).

We know that diagonals of a rhombus cut each other at right angles. So ΔAOB is a right angled triangle.

Using Pythagoras theorem in ΔAOB, we get

$OA^2+OB^2=AB^2$

$4^2+x^2=5^2$

$16+x^2=25$

$x^2=25-16$

$x^2=9$

$x=\sqrt{9}$

x = 3 cm

Thus the length of another diagonal BD is,

BD = 2x = 6 cm.

Therefore the area of the rhombus is given by,

Area of rhombus =$\frac{1}{2}\times (poduct of diagonals)$

Area(ABCD) = $\frac{1}{2}\times AC\times BD$

                    = $\frac{1}{2}\times 8\times 6$

                    = $24 cm^2$

Area of a rhombus is 24 $cm^2$.