Q. 26

# Find 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.

Answer :

Given:

AC = 15 cm

AB = 17 cm

AD = 9 cm

CD = 12 cm

In ∆ACB (right-angled),

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

⇒ BC^{2} + AC^{2} = AB^{2}

⇒ BC^{2} = AB^{2} - AC^{2}

⇒ BC^{2} = 17^{2} - 15^{2}

⇒ BC^{2} = 289 - 225

⇒ BC^{2} = 64

⇒ BC= 8 cm

Area of ∆ACB = 1/2 × BC × AC

= 1/2 × 8 cm × 15 cm

= 60 cm^{2}

In ∆ADC,

Area of ∆ADC = 1/2 × AD × CD

= 1/2 × 9 cm × 12 cm

= 54 cm^{2}

Now,

Area of quadrilateral ABCD = Area of ∆ACB + Area of ∆ADC

= 60 cm^{2} + 54 cm^{2}

= 114 cm^{2}

And,

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

= 17 cm + 8 cm + 12 cm + 9 cm

= 46 cm

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PREVIOUSFind 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.]NEXTFind the area of the quadrilateral ABCD in which AB = 42 cm, BC = 21 cm, DA = 34 cm and diagonal BD = 20 cm.

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