Area of General Quadrilateral

To find the area of any quadrilateral we can divide it into two triangles and then the area can be easily calculated by calculating the area of both the triangles separately.

\mathrm{Area\ of\ ABCD = Area\ of\ \Delta ABC + Area\ of\ \Delta ACD}

\mathrm{= \left(\dfrac{1}{2}\right) \times AC \times h_1+ \left(\dfrac{1}{2}\right) \times AC\times h_2}

Area of quadrilateral \mathrm{=\dfrac{1}{2}(h_1+h_2)d}

Where hand h2 are the height of both the triangles and d is the length of common diagonal i.e.AC.

Example

Find the area of quadrilateral ABCD.

Solution:

In the quadrilateral ABCD,

BD is the common diagonal so d=5\ cm .

Height of the two triangles are h_1=2\ cm and  h_2=1\ cm.

Area of quadrilateral ABCD \mathrm{=\dfrac{1}{2}\times(h_1+h_2)d}

=\dfrac{1}{2}(5)(2+1)

\mathrm{=7.5\ cm^2}

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