1. **State the problem:** We need to find the lengths of the bases $AB$ and $DC$ of the isosceles trapezoid $ABCD$ to calculate its perimeter. 2. **Given information:** - $WY$ is the midsegment of trapezoid $ABCD$. - $WY = 12.6$. - $BY = 4.24$. - $AD = BC$ (isosceles trapezoid). 3. **Recall the midsegment property of trapezoids:** The midsegment length $WY$ is the average of the lengths of the two bases: $$WY = \frac{AB + DC}{2}$$ 4. **Use the formula to find $AB + DC$:** Multiply both sides by 2: $$2 \times WY = AB + DC$$ $$2 \times 12.6 = AB + DC$$ $$25.2 = AB + DC$$ 5. **Find the perimeter:** The perimeter $P$ of trapezoid $ABCD$ is: $$P = AB + BC + CD + DA$$ Since $AD = BC$, let $AD = BC = x$. 6. **Find $x$ using given lengths:** Given $BY = 4.24$ and $BY \cong CY$, and $WY$ is the midsegment, the legs $AD$ and $BC$ are equal. Assuming $WD = 4.24$ (from problem statement), then $AD = BC = 4.24$. 7. **Calculate perimeter:** $$P = AB + BC + CD + DA = (AB + DC) + 2 \times AD = 25.2 + 2 \times 4.24 = 25.2 + 8.48 = 33.68$$ **Final answers:** - $AB + DC = 25.2$ - Perimeter $P = 33.68$