Answer:
Area= 54 cm^2
Step-by-step explanation:
Recall that a rhombus is given by the product of its two diagonals (d1 and d2) divided by 2.
Area = d1 * d2 / 2
So in our case, the longer diagonal is 12 cm long, and the shortest one should be in the ratio 3:4, therefore:
3 /4 = d2 / d1
3 / 4 = d2 / 12
d2 = 3 * 12 /4
d2 = 3 * 3
d2 = 9 cm
Then we can now calculate the Area of the rhombus as;
Area = d1 * d2 / 2 = 12 * 9 / 2 = 54 cm^2
