in rhombus ABCD AC=16cm, AB=10cm, find its area
http://www.wikihow.com/Calculate-the-Area-of-a-Rhombus
To find the area of a rhombus, you can use the formula:
Area = (diagonal1 * diagonal2) / 2
In this case, we need to find the diagonals first.
Since the diagonals of a rhombus bisect each other at right angles, we can use the Pythagorean theorem to find the length of the diagonals.
Let's assume that the diagonals are AC and BD.
Using the given information, we know that AC = 16cm and AB = 10cm.
To find the length of BD, we can use the Pythagorean theorem:
BD^2 = AC^2 - AB^2
BD^2 = 16cm^2 - 10cm^2
BD^2 = 256cm^2 - 100cm^2
BD^2 = 156cm^2
Taking the square root of both sides, we can find the length of BD:
BD = √156 cm
Since the diagonals of a rhombus are perpendicular bisectors of each other, we can also find the length of the other diagonal using the same method.
Let's assume that the other diagonal is DB.
Using the given information, we know that AB = 10cm and AC = 16cm.
To find the length of DB, we can use the Pythagorean theorem:
DB^2 = AC^2 - AB^2
DB^2 = 16cm^2 - 10cm^2
DB^2 = 256cm^2 - 100cm^2
DB^2 = 156cm^2
Taking the square root of both sides, we can find the length of DB:
DB = √156 cm
Now that we have both diagonals, we can calculate the area using the formula:
Area = (diagonal1 * diagonal2) / 2
Area = (√156 cm * √156 cm) / 2
Simplifying this expression, we get:
Area = (156 cm) / 2
Area = 78 cm^2
Therefore, the area of the rhombus ABCD is 78 square cm.
To find the area of a rhombus, you need to know the length of one side and the length of the altitude (perpendicular height) of the rhombus.
In this case, we know that AC = 16 cm, but we do not have the altitude directly given. However, we can use the Pythagorean theorem to find it.
Since ABCD is a rhombus, the diagonals are perpendicular bisectors of each other. AB and AC are diagonal of the rhombus, and they intersect at point A. Let E be the point of intersection of both diagonals.
According to the Pythagorean Theorem, in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. We can use this theorem to find the altitude.
First, we find the length of the altitude. From point A, draw a perpendicular line to line BC, calling the point of intersection F. Triangle AFB is a right-angled triangle. The hypotenuse is AB with length 10 cm, and one of the legs is half of AC, which is 8 cm (since the diagonals bisect each other). Using the Pythagorean theorem:
AF^2 + FB^2 = AB^2
AF^2 + 8^2 = 10^2
AF^2 + 64 = 100
AF^2 = 100 - 64
AF^2 = 36
AF = √36
AF = 6 cm
Now, we have the length of the altitude, which is 6 cm.
To calculate the area of the rhombus, you can use the formula:
Area = base * height
Since the base is one side of the rhombus, which is 10 cm, and the height is the altitude, which is 6 cm, the area of the rhombus is:
Area = 10 cm * 6 cm
Area = 60 cm^2
Therefore, the area of the given rhombus is 60 square centimeters.
half length of diagonal = 8
look at B to center of that diagonal
now have 8, 6, 10 right triangle
area of that triangle = (1/2)8 *6
there are 4 of those trianges on the rhombus
16 * 6 = 96
or half product of diagonals
(1/2)(16*12) = 96