Question

Perimeter of rhombus is 90cm. One of its diagonal is 30cm, find the area.

Answer 1

Answer:

Diagonal 1 = 30 cm

Perimeter of rhombus = 90 cm

∴ Side of rhombus = 90/4

                               = 22.5 cm

∴ Hypotenuse = 22.5 cm

∴ Altitude = 30 cm/2 = 15 cm

Hypotenuse² = a² + b²

= 22.5² = 15² + b²

= 506.25 = 225 + b²

= 506.25 - 225 = b²

= 281.25 = b²

= √281.25 = b

= 16.7 cm = b

∴ Diagonal 2 = 16.7 + 16.7 = 33.4 cm

∴ Area of rhombus = 1/2 x d x d

                               = 1/2 x 30 x 33.4

                               = 15 x 33.4

                               = 501 cm²