+1310 A rhombus has a perimeter of 68 units and one of its diagonals is 30 units. What is its area in square units?
+128731 The side of the rhombus = 68 / 4 = 17
And the diagonals meet at right angles. So....one side and (1/2) of the length of any diagonal form two sides of a right triangle, with the side forming the hypotenuse and the half-diagonal forming a leg.
So the remaining leg is formed by the other (1/2) diagonal and is given by √[17^2 - 15^2] = √[289 - 225] = √64 = 8. So the other diagonal = 16.
And....the total area will be given by (1/2)ab where a is the length of one diagonal and b is the length of the other......so we have....
(1/2)(30)(16) = 240 sq. units
+128731 The side of the rhombus = 68 / 4 = 17
And the diagonals meet at right angles. So....one side and (1/2) of the length of any diagonal form two sides of a right triangle, with the side forming the hypotenuse and the half-diagonal forming a leg.
So the remaining leg is formed by the other (1/2) diagonal and is given by √[17^2 - 15^2] = √[289 - 225] = √64 = 8. So the other diagonal = 16.
And....the total area will be given by (1/2)ab where a is the length of one diagonal and b is the length of the other......so we have....
(1/2)(30)(16) = 240 sq. units
