Find the area of the rhombus: In rhombus ABCD, AB=11 and AC=13. Find the area of the rhombus.

What should be done to find the values of the diagonals?

For a rhombus (equal sides), AB = BC.

AC is already one diagonal that you know. The other is
BD = 2*sqrt(11^2 -6.5^2) = 17.75
The area is half the product of the diagonals.

What does 2*sqrt mean?

2 times the square root of( )

In rhombus ABCD, AB=20 and AC=25. Find the area of the rhombus to the nearest tenth.

To find the values of the diagonals in a rhombus, you can use the Pythagorean theorem or the formula for the area of a triangle.

In a rhombus, the diagonals are perpendicular bisectors of each other, dividing the rhombus into four congruent right triangles. Therefore, you can use the Pythagorean theorem to find the length of the diagonals.

In this case, we are given that AB = 11 and AC = 13. Since a rhombus has congruent sides, we know that AB = BC = CD = DA. To find the length of the diagonal BD, we need to use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the right triangle is ABD, where AB is the base, BD is the hypotenuse, and AD is the height. Using the Pythagorean theorem, we have:

BD^2 = AB^2 + AD^2

Since AB = 11 and AD = AC/2 = 13/2 = 6.5, we can substitute these values into the equation:

BD^2 = 11^2 + 6.5^2

Simplifying, we get:

BD^2 = 121 + 42.25
BD^2 = 163.25

Taking the square root of both sides, we find:

BD ≈ √163.25

Therefore, the length of the diagonal BD is approximately equal to the square root of 163.25.

Similarly, to find the length of the other diagonal, AC, we can use the same process. Since AC = 13, and BC is also a side of the rhombus, we can use the Pythagorean theorem with right triangle ABC:

AC^2 = AB^2 + BC^2

Substituting the given values, we have:

13^2 = 11^2 + BC^2

BC^2 = 169 - 121
BC^2 = 48

Taking the square root of both sides, we find:

BC = √48

Therefore, the length of the diagonal AC is equal to the square root of 48.

Now that we have the lengths of the diagonals, we can find the area of the rhombus using the formula:

Area = (diagonal1 * diagonal2) / 2

In this case, diagonal1 = BD ≈ √163.25 and diagonal2 = AC = √48. Substituting these values into the formula, we have:

Area = (√163.25 * √48) / 2

Simplifying, we get:

Area ≈ (12.78 * 6.93) / 2
Area ≈ 88.46 / 2
Area ≈ 44.23

Therefore, the area of the rhombus is approximately 44.23 square units.