Question

 A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, what is the area of the field? एक समचर्तुभुज आकार के खेत में 18 गायों को चराने के लिए हरी घास है। यदि इस समचर्तुभुज की हरेक भुजा 30 मीटर है और उस का बड़ा विकर्ण 48 मीटर है, तो इस खेत का क्षेत्रफल क्या होगा? *

1728 ਵਰਗ ਮੀ.sq m वर्ग मीटर

864 ਵਰਗ ਮੀ.sq m वर्ग मीटर

432 ਵਰਗ ਮੀ.sq m वर्ग मीटर

210.5 ਵਰਗ ਮੀ.sq m वर्ग मीटर

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Answer 1

Answer:

864 m² is the area of that field

Answer 2

Let the diagonals AC & BD intersect at O.

therefore AO=CO (property of rhombus)

and also BO=CO

Let the longer diagonal is AC=48m

therefore AO=CO= 1/2 × 48

theredore AO=CO=24m

For triangle AOB

AB^2 = OA^2 + OB^2 (Pythagoras Theorem)

30^2 = 24^2 + OB^2

OB^2 = 900-576

OB^2 = 324

OB = 18m = CO

OB+OC=BC

therefore BC = 18 + 18 = 36

Now,

Area of rhombus = 1/2 × d1 × d2

= 1/2 × 48 × 36

= 48 × 36

2

= 1728

2

= 864m^2

Now,

Total no. of cows = 18

Area of grass field = 864m^2

therefore each cow will get = 864/18

= 48m^2

First of all the shape of the garden is rhombus. So the diagonals in a rhombus bisect each other at 90°.

First of all the shape of the garden is rhombus. So the diagonals in a rhombus bisect each other at 90°. And also if AC & BD intersect at O then AO=CO & BO=DO.

First of all the shape of the garden is rhombus. So the diagonals in a rhombus bisect each other at 90°. And also if AC & BD intersect at O then AO=CO & BO=DO. All sides of a rhombus are equal.