A park, in the shape of a quadrilateral $A B C D$ , has $∠ C = 90^{o}, A B = 9 m, B C = 12 m, C D = 5 m, A D = 8 m$ . How much area does it occupy?( Write the first digit before decimal point)

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Solution

$s = \frac{9 + 8 + 13}{2}$
$= 15$
$B D = \sqrt{(12)^{2} + (5)^{2}} = 13$
$A r . A B C D = A r B C D + A r A B D$
$= \frac{1}{2} (12) (5) + \sqrt{s (s - 8) (s - 9) (s - 13)}$
$= 30 + \sqrt{(15) (7) (6) (2)}$
$= 30 + 6 \sqrt{35} m^{2}$
$= 65.49 m^{2}$

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