find the perimeter of the polygon if ∠b≅∠d.\np = ? cm
find the perimeter of the polygon if ∠b≅∠d.\np = ? cm
Answer
Explanation:
Step1: Recall tangent - segment property
If a quadrilateral is circumscribed about a circle, then the sum of the lengths of opposite sides are equal. Given (\angle B\cong\angle D), the quadrilateral (ABCD) is circumscribed about a circle. Let the lengths of the sides be (AB = 6.5\mathrm{cm}), (BC=7.5\mathrm{cm}), (CD = 8.5\mathrm{cm}), and (DA=x\mathrm{cm}). According to the property of a circum - scribed quadrilateral (AB + CD=AD + BC).
Step2: Solve for the unknown side
We know that (6.5+8.5=x + 7.5). [ \begin{align*} 15&=x + 7.5\ x&=15 - 7.5\ x&=7.5 \end{align*} ]
Step3: Calculate the perimeter
The perimeter (P) of a quadrilateral with side lengths (a,b,c,d) is (P=a + b + c + d). Here (a = 6.5\mathrm{cm}), (b = 7.5\mathrm{cm}), (c = 8.5\mathrm{cm}), (d = 7.5\mathrm{cm}). So (P=6.5+7.5 + 8.5+7.5). [ \begin{align*} P&=(6.5+8.5)+(7.5 + 7.5)\ &=15+15\ &=30 \end{align*} ]
Answer:
(30)