Question

A land is in the shape of rhombus. the perimeter of the rhombus is 160m. and one of its diagonal is 48. find its area

Answer 1

Answer:

Step-by-step explanation:

Length of one side of a rhombus = 160/4 = 40 m

the length of other diagonal2= 40²-24²    (48/2=24)

                                                = 1600 - 576

                                                =1024m²

                                               =32

                                               =32*2 = 64m

area of rhombus =48*64/2

                           =1536m²

∴the area of rhombus is 1536m².

Answer 2

Area of the land is given by 1536 m²

Step-by-step explanation:

In the attached figure ABCD is a rhombus and AC and BD are diagonals.

The perimeter of a rhombus is four times its side length.

Hence,

4CD = 160

CD = 160/40

CD = 40 m

And the diagonals of a rhombus bisects each other at 90 degrees.

Hence,

OC = 48/2

OC = 24 m

In right triangle ODC, applying Pythagoras theorem,

$OD=\sqrt{40^2-24^2}\\\\OD=32$

Hence, length of the diagonal BD = 2×32 = 64 m

Therefore, area of rhombus is given by

$A=\frac{1}{2}(AC\times BD}\\\\A=\frac{1}{2}(64\times48}\\\\A=1536 m^2$

#Learn More:

If a triangle and a  rhombus are on the same base and between the parallels,find the ratio of area of triangle and area of triangle and area of rhombus.

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