Question

find the side of a rhombus whose area is 24 and it's diagonals is 6 and 8 cm.​

Answer 1

The area of a rhombus is equal to the half of the product of its diagonals.

A = (d1 * d2)/2

• 24 cm^2 = (8 cm * d2)/2

• 24 * 2 cm^2 = 8 cm * d2

(24 * 2 / 8) (cm^2/cm) = d2

• 6 cm = d2

Why is A = (d1 * d2) / 2? =

The rhombus may be fit into a rectangle as shown above (note that the measurements are not exact). One diagonal may represent the height of the rectangle and the measure of the other diagonal equals the horizontal sides of the rectangle. Each of the smaller rectangles were halved by a side of the rhombus (green). Therefore, the area of the rhombus is only half of the area of the rectangle that it fit in.