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.

Given:

AC = 15 cm

AB = 17 cm

CD = 12 cm

In ∆ACB (right-angled),

Base2 + Perpendicular2 = Hypotenuse2

BC2 + AC2 = AB2

BC2 = AB2 - AC2

BC2 = 172 - 152

BC2 = 289 - 225

BC2 = 64

BC= 8 cm

Area of ∆ACB = 1/2 × BC × AC

= 1/2 × 8 cm × 15 cm

= 60 cm2

= 1/2 × 9 cm × 12 cm

= 54 cm2

Now,

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

= 60 cm2 + 54 cm2

= 114 cm2

And,

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

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

= 46 cm

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