Question

Find area of rhombus with length of its side 30cm and larger diagonal 48cm.​

Answer 1

Step-by-step explanation:

The diagonals of a rhombus are perpendicular ie at 90 degrees to one another.

Half the lengths of the diagonals form a right-angled triangle with one side of the rhombus as the hypotenuse.

Let the length of the side of the rhombus be s and s = 30: 30^2 = (48/2)^2 + (d/2)^2 = 24^2 + d^2 /4 .

900 = 576 + d^2 /4 => d^2 /4 = 900 - 576 = 324.

d^2 = 324 x 4 = 1 296 => d = 36.

Area of rhombus = (1/2)(48)(36) = 864 sq cm.