Question

find the perimeter of the following polygon​

Answer 1

Answer:

48cm

Step-by-step explanation:

let the name of the middle point measuring 90° be O

using the pythagoras theorem for ΔABO

AB² + BO² = AO²

3² + 4² = AO²

9 + 16 = AO²

25 = AO²

AO = √25 = 5cm

using the pythagoras theorem for ΔDCO

DC² + DO² = OC²

9² + 12² = OC²

81 + 144 = OC²

225 = OC²

OC = √225 = 15cm

perimeter of polygon = 3cm + 4cm + 15cm + 9cm + 12cm + 5cm = 48cm

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Answer 2

Answer:

In ∆ ABO,

AO² = AB² + BO² (Pythagoras theorem)

AO² = 3² + 4²

AO² = 9 + 16

AO² = 25

AO = √25

AO = 5 cm.

Now, in ∆ DCO,

OC² = DC² + DO²

OC² = 9² + 12²

OC² = 81 + 144

OC² = 225

OC = √225

OC = 15 cm.

Perimeter of polygon = (3 + 4 + 5 + 12 + 9 + 15) cm

= 48 cm.