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]

Answer 1

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

Area of Quadrilateral = 60.66 ${cm}^2$

Consider $\Delta ABC$

S = $\frac{Perimeter}{2}$ = $\frac{10+8+6}{2}$ = 12 cm

Area = $\sqrt{s(s-a)(s-b)(s-c)}$

Area = $\sqrt{12(12-10)(12-8)(12-6)}$

Area = $\sqrt{576}$ = 24${cm}^2$

Now Area of $\Delta CDA$ = 60.66-24 = 36.66

Now consider $\Delta CDA$

S = $\frac{Perimeter}{2}$ = $\frac{10+8+x}{2}$ = $\frac{18+x}{2}$ cm

Now Area = 36.66 = $\sqrt{s(s-a)(s-b)(s-c)}$

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

$x=10cm$