GEOMETRY: Find the perimeter of the polygon if Angle B is congruent to Angle D

Given:

∠B ≅ ∠D

AB = 11.5 cm

To find:

The perimeter of the polygon.

Solution:

The reference image for the answer is attached below.

AP and AS are tangents drawn from the external point A.

BP and BQ are tangents drawn from the external point B.

CQ and CR are tangents drawn from the external point C.

DR and DQ are tangents drawn from the external point D.

If two tangents drawn from an same external point to a circle, then the lengths of tangents are equal.

⇒ AP = AS,   BP = BQ,   CQ = CR,   DR = DS

AS = 11.5 cm

BP = BQ

BP = 12.5 cm

CQ = CR

CQ = 13.5 cm

Given ∠B ≅ ∠D

⇒ DS = DR = 12.5 cm

Perimeter of polygon = AP + BP + BQ + CQ + CR + DR + DS + AS

                                    = 11.5 + 12.5 + 12.5 + 13.5 + 13.5 + 12.5 + 12.5 + 11.5

                                    = 100

The perimeter of the polygon is 100 cm.

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step-by-step explanation: