Q. 25

# Find the area of the quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90° and ΔBCD is an equilateral triangle having each side equal to 26 cm. Also find the perimeter of the quadrilateral. [Give: √3 = 1.73.]

Answer :

Given:

BC = 26 cm

DC = 26 cm

AD = 24 cm

BD = 26 cm

In ∆BCD,

= 292.37 cm^{2}

In ∆ADB,

Base^{2} + Perpendicular^{2} = Hypotenuse^{2}

⇒ AB^{2} + AD^{2} = DB^{2}

⇒ AB^{2} = DB^{2} - AD^{2}

⇒ AB^{2} = 26^{2} - 24^{2}

⇒ AB^{2} = 676 - 576

⇒ AB^{2} = 100

⇒ AB= 10 cm

Area of ∆ADB = 1/2 × AB × AD

= 1/2 × 10 cm × 24 cm

= 120 cm^{2}

Now,

Area of quadrilateral ABCD = Area of ∆ADB + Area of ∆BCD

= 120cm^{2} + 292.37 cm^{2}

= 412.37 cm^{2}

And,

Perimeter of quadrilateral ABCD = AB + BC + CD + DA

= 10 cm + 26 cm + 26 cm + 24 cm

= 86 cm

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PREVIOUSIn the given figure, ABCD is a quadrilateral in which diagonal BD = 24 cm, AL ⊥ BD and CM ⊥BD such that AL = 9 cm and CM = 12 cm. Calculate the area of the quadrilateral.NEXTFind the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, ∠ACB = 90° and AC = 15 cm.

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