To find the area of a rhombus, one needs the lengths of both diagonals since the area of a rhombus is pq/2, given that p and q are both diagonals.
Given: BK is 3, so BD is 6. We already have one diagonal.
Using the lengths given (BK=3 and BC=5) and the fact that BKC is a right triangle, we can use Pythagorean Theorem to solve for the missing leg of the right triangle.
Pythagorean Theorem: a^2+b^2=c^2, given that a and b are the legs of the triangle and c is the hypotenuse.
Plug in the given values: a^2+3^2=5^2
a^2+9=25
Subtract 9 from both sides.
a^2=16
Square root both sides.
a=4
Now we know that side a of the right triangle, or segment CK, is 4 units long. Since K is the midpoint of the rhombus, the diagonal AC is 8 units long.
Now, we know that the diagonals lengths are 6 and 8. We can plug these into the rhombus area formula to find the area.
6*8/2=A
48/2=A
24=A
The area is 24 square units.
I hope this helps :)