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The area of triangle AXD can be calculated directly as half the area of the square since the base is AD and the perpendicular height is AB. 

½ × 6 × 6 = 18 cm²

 

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(a) Area of Δ ABX + Area Δ DCX 

= 0.5 x (BX) x 6 + 0.5 x (XC) x 6 

= 3 (BX) + 3 (XC)

= 3 (BX + XC)  =  3 x 6   = 18 cm²

   Area of Δ AXD 

= Area of Square ABCD – (sum of Area of Δ ABX + Area Δ DCX )

= 36 – 18 = 18 cm²

 

(b) Area of Δ AXD   = 0.5 x AX x AZ 

     18  = 0.5 x AX x 5

     AX = 7.2  cm²

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