Area of a special quadrilateral (Rhombus) — lesson. Mathematics CBSE, Class 8.

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A special quadrilateral is nothing but a rhombus. To find the area of a rhombus, we can use the same triangulation method as used in finding the area of a general quadrilateral.

A rhombus after triangulation is given below.

From the figure given above, we can come to the following inferences.

$ABCD$ is a rhombus with diagonals

$AC$ and

$BD$ .

Let

$AC$ be

$d_1$ and

$BD$ be

$d_2$ . The diagonals

$d_1$ and

$d_2$ intersect at

$O$ .

Also, as per the properties of a rhombus, the diagonals bisect each other.

$\text{Area of the rhombus}$

$ABCD =$

$(\text{Area of}$

$\triangle ABD))$

$+$

$(\text{Area of}$

$\triangle BCD)$

$=$

$\frac{1}{2} \times BD \times OA$

$+$

$\frac{1}{2} \times BD \times OC$

$=$

$\frac{1}{2} \times BD \times (OA + OC)$

$=$

$\frac{1}{2} \times BD \times AC$

[Since

$AC = OA + OC$ ]

$=$

$\frac{1}{2} \times d_1 \times d_2$

[Since we have assumed that

$AC = d_1$ , and

$BD = d_2$ ]

Therefore,

$\text{area of a rhombus} = \frac{1}{2} \times d_1 \times d_2$ square units or the area of the rhombus is half the product of its diagonals.

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2. Area of a special quadrilateral (Rhombus)

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