What is the area of the rhombus in simplest radical form? The figure is not drawn to scale.
Image: www(dot)connexus(dot)com/content/media/226250-9182012-41015-PM-1902891586(dot)jpg
a. 50
b. 10√3
c. 25√6
d. 50√3
We can find the area of a rhombus by multiplying its diagonals and dividing by 2. The length of one diagonal is 10 (given) and the length of the other diagonal can be found using the Pythagorean theorem in triangle DEF:
DE² + EF² = DF²
8² + 6² = DF²
64 + 36 = DF²
100 = DF²
DF = 10√2
So the area of the rhombus is:
(10)(10√2)/2 = 50√2
This cannot be simplified further, so the answer is not one of the choices given.
So, the most possible answer could be either D?
No, D is not a possible answer because the answer choices are all in simplest radical form and 50√2 cannot be simplified any further. The correct answer is not one of the choices given.
What about A?
No, A is not a possible answer either, since 50 is not in its simplest form (it can be simplified by dividing both the numerator and denominator by 2).
Therefore, the correct answer is not given among the answer choices.
To find the area of a rhombus, we can use the formula:
Area = (diagonal 1 * diagonal 2) / 2
In the given image, it is not clear which lengths are the diagonals. Therefore, we cannot calculate the area with certainty based on the information provided.
To find the area of a rhombus, you can use the formula: Area = (diagonal1 * diagonal2) / 2.
Looking at the provided image, we can see that the length of diagonal1 is 10 units, and the length of diagonal2 is 2√3 units.
Now, substitute these values into the formula: Area = (10 * 2√3) / 2.
Simplifying this expression, we have: Area = 20√3 / 2.
Further simplifying, we divide both the numerator and the denominator by 2: Area = 10√3.
Therefore, the area of the rhombus in simplest radical form is option b: 10√3.