the perimeter of rhombus is328 and one diagonal is 160 cm.find the area
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Since all sides are equal in a rhombus then it's perimeter = 4 × side,now the perimeter is given
328 = 4 × side =>side = 328/4 = 82.We may use Pythagoras theorem the calculate half of the other diagonal.Then,our hypotenuse = 82 and perpendicular = 160/2=80.
82^2 - 80^2 = half of the other diagonal^2
=> √324 = half of the other diagonal.
half of the other diagonal = 18
the whole diagonal = 2 times its half
=>2 × 18 = 36
We know that diagonal × the other diagonal / 2 = area
36 × 160 /2 = 36 × 80 = 2,880 cm^2 is your answer.
328 = 4 × side =>side = 328/4 = 82.We may use Pythagoras theorem the calculate half of the other diagonal.Then,our hypotenuse = 82 and perpendicular = 160/2=80.
82^2 - 80^2 = half of the other diagonal^2
=> √324 = half of the other diagonal.
half of the other diagonal = 18
the whole diagonal = 2 times its half
=>2 × 18 = 36
We know that diagonal × the other diagonal / 2 = area
36 × 160 /2 = 36 × 80 = 2,880 cm^2 is your answer.
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