What is the area of a rhombus if its diagonals are 10 and 16?
A rhombus is a flat geometric figure, a parallelogram, in which all four sides are equal. In the figure ABCD – a rhombus, its sides AB, BC, CD and AD are equal.
The diagonals of a rhombus are the line segments that connect the vertices of its opposite corners. In Figure BD and AC are the diagonals of the rhombus. Basic properties of diagonals:
intersect at right angles: BD ┴ AC;
are the bisectors of the rhombus angles: ∠BAC = ∠BCA or ∠ABD = ∠CBD;
divide the rhombus into four right-angled triangles equal to each other: △ BOC = △ COD = △ AOD = △ AOB;
the sum of the squares of the diagonals equals the square of either side, quadrupled: BD ^ 2 + AC ^ 2 = 4AB ^ 2.
The area of a rhombus is the area of the space bounded by the sides of the rhombus. The area formula through two diagonals is written as follows:
S = 1/2 * d1 * d2,
where S is the area of the rhombus,
d1 – the length of one diagonal of the rhombus,
d2 – the length of the second diagonal of the rhombus.
Determine the area of a rhombus with diagonals 10 and 16 cm
Given a rhombus ABCD. By the property of a rhombus, its sides are equal:
AB = BC = CD = AD.
By the condition of the problem, AC and BD are the diagonals of the rhombus:
AC = 16 cm,
ВD = 10 cm.
It is necessary to find the area of the rhombus. To do this, we will use the formula for finding the area through the diagonals of a rhombus:
S = 1/2 * d1 * d2,
Sabcd = 1/2 * AC * BD.
Substitute the known values into the formula and calculate the area:
Sabcd = 1/2 * 10cm * 16cm = 80 kV cm.
Answer: The area of the ABCD rhombus is 80 kV. Cm.
