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I’m confused on this one

I’m confused on this one-example-1
User Implmentor
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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 :)

User Zarruq
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