Question

A park, in the shape of a quadrilateral ABCD, has ∠C = 90°, AB = 9m,BC = 12m,CD = 5m and AD = 8 m.
How much area does it occupy?​

Answer 1

Answer:

Join BD in ΔBCD,   BC and DC are given.

So, we can calculate BD by applying Pythagoras theorem

⇒BD=BC²+CD²

​ =12²+5²

=144+25

​ =13 m=BD

⇒Area of □ABCD= Area of ΔABD+ Area of ΔBCD

⇒Area of ΔBCD

=21​×b×h= 1/2​×12×5

= 30 m²

⇒Area of ΔABD

=s(s−a)(s−b)(s−c)

​ (Heron's formula)

⇒2S=9+8+13, S=30​/2

⇒S=15  m

⇒Area of ΔABD

= 15(15−9)(15−8)(15−13)

​= 15×6×7×2

​= 630×2

​=6√1260

​=35.49m²

⇒Area of Park = Quad ABCD

= 30+35.49

= 65.49  m² = 65.5  m²

Answer 2

Step-by-step explanation:

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