Find the area of the quadrilateral ABCD in which AD = 42 cm , = 90^{0} and is an equilateral triangle having each side equal to 26 cm. Also, find the perimeter of the quadrilateral. [Given = 1.73]

Let us consider a right triangle ABD,

By using Pythagoras theorem in this, we get

AB =

=

=

= 10 cm

We know that,

Area of triangle =

=

= 120 cm^{2}

We also know that,

Area of an equilateral triangle BCD = sq units

=

= 292.37 cm^{2}

Therefore,

Area of quadrilateral ABCD = Area of triangle ABD + Area of triangle BCD

= 120 + 292.37

= 412.37 cm^{2}

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