Question

The length of a side and diagonal of a rhombus is 13 m and 10 m respectively. Find the area of the rhombus. plz answer with correct explanation​

Answer 1

Step-by-step explanation:

We have ABCD is the rhombus in which

length of the rhombus = 13m

diagonal of the the rhombus = 10m

here, AB= 13m and diagonal BD = 10m

At first we have to find the other diagonal of this rhombus because we know that the area of a rhombus is 1/2(d1 X d2) units²

so, let draw the diagonal CA so that the two diagonals intersect at one point.

Now name the intersection point be O.

Now in traingle OAB, we have-

AB = 13m

OB = 1/2 of BD as (the diagonals of a rhombus bisects each other at right angle.) = 5m

we have to find OA

We know that the diagonals bisects eachother at 90° so traingle OAB is a right angled traingle.

So, (OA)² + (OB)² = (AB)² Pythagoras theorem

= (OA)² = (AB)²-(OB)²

= (OA)² = 13²-10²

= (OA)² = 69

= OA = √69

OA = 1/2 AC

So the length of other diagonal will be 2√69m

now,the area = 1/2 X BD X AC

= 1/2 X 10 X 2√69

= 10√69 m²

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