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Question

In a quadrilateral ABCD AB = 6 cm, BC = 8 cm, CD = 8 cm and AC=10cm.The area of the quadrilateral is 60.67 cm2. Find DA.
[4 MARKS]

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Solution

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Area of Quadrilateral = 60.66 cm2


Consider ΔABC

S = Perimeter2 = 10+8+62 = 12 cm

Area = s(sa)(sb)(sc)

Area = 12(1210)(128)(126)

Area = 576 = 24cm2


Now Area of ΔCDA = 60.66-24 = 36.66


Now consider ΔCDA


S = Perimeter2 = 10+8+x2 = 18+x2 cm

Now Area = 36.66 = s(sa)(sb)(sc)


Now by putting value of s, a, b and c

x=10cm


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