Question

How to find the area of this quadrilateral?

Answer 1

Hint: Here in this question, we have to find the area of the given quadrilateral. For this, first we need to partition or divide the given quadrilateral as two triangles then find the area of the two triangles using the formula of area of triangle then their sum gives the required area of the given figure.

Complete step by step answer:
Quadrilateral, which is a flat closed two-dimensional shape having 4 straight sides. The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e.,
$Area(A) = \dfrac{1}{2} \times base \times height$
$\Rightarrow A = \dfrac{1}{2} \times b \times h$.
Hence, to find the area of a tri-sided polygon, we have to know the base (b) and height (h) of it.

Consider the given question: we need to find the area of this quadrilateral $ABCD$:

The area of quadrilateral $ABCD$ $ = $ area of triangle $\vartriangle \,ABC$ $ + $ area of triangle $\vartriangle \,ADC$ ----- (1)
The area of quadrilateral $ABCD$ $ = $ $\dfrac{1}{2} \times BE \times AC$ $ + $ $\dfrac{1}{2} \times DF \times AC$
The area of quadrilateral $ABCD$ $ = $ $\dfrac{1}{2} \times AC\left( {BE + DF} \right)$
By the figure, $BE = DF = 6\,cm$ and $AC = 18\,cm$, then
The area of quadrilateral $ABCD$ $ = $ $\dfrac{1}{2} \times 18\left( {6 + 6} \right)$
The area of quadrilateral $ABCD$ $ = $ $9\left( {12} \right)$

Hence, the area of quadrilateral $ABCD$ $ = $ $108\,\,c{m^2}$.

Note: While determining the area we use the formula. The formula is $A = \dfrac{1}{2} \times b \times h$. The unit for the perimeter will be the same as the unit of the length of a side or triangle. Whereas the unit for the area will be the square of the unit of the length of a triangle. We should not forget to write the unit.