Question

Find the perimeter of the polygon

Answer 1

Answer:

The perimeter of the polygon is 48 cm.

Step-by-step explanation:

Given: $\angle B \cong \angle D$

To find the perimeter of the polygon, we need to find the lengths of the AB, BC, CD and DA

Since, $\angle B \cong \angle D$ and to find the length, from circle theorem, "Two tangents from an external point to a circle are always equal in length".

From this statement we shall conclude,

The length of $AB=5+6=11$

The length of $BC=6+7=13$

The length of $CD=7+6=13$

The length of $DA=6+5=11$

Thus, the perimeter of the polygon is

$\begin{aligned}\text {Perimeter} &=A B+B C+C D+D A \\&=11+13+13+11 \\&=48 \mathrm{cm}\end{aligned}$

Hence, the perimeter of the polygon is 48 cm.