Question

Find the area of a rhombus whose perimeter is 200 m and one of the diagonal is 80 metre

Answer 1

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Answer 2

Answer:

The area of rhombus is 2400 meter square.

Step-by-step explanation:

Given : A rhombus whose perimeter is 200 m and one of the diagonal is 80 meter.

To find : The area of a rhombus?

Solution :

Let the sides of the rhombus be A,B,C,D

We have given,The perimeter of rhombus

i.e, AB+BC+CD+DA=200 m

Sides of rhombus are equal

∴ 4AB=200

AB=50 m

Each side of rhombus is AB=BC=CD=DA=50 m

Refer the attached figure below.

Diagonal AC=80 m

A0=40 m

In ΔAOB, ∠AOB=90°

Applying Pythagoras theorem in ΔAOB,

$OB^2=AB^2-AO^2$

$OB^2=50^2-40^2$

$OB^2=2500-1600$

$OB=\sqrt{900}$

$OB=30$

BD=2(OB)=2(30)=60 m

Area of rhombus ABCD= product of diagonals divided by 2

$A=\frac{AC\times BD}{2}$

$A=\frac{80\times 60}{2}$

$A=2400m^2$

Therefore, The area of rhombus is 2400 meter square.