Subjects geometry

Trapezoid Area A16C88

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1. **Problem Statement:** We have a trapezoid with two vertical sides labeled $y$ inches and $x$ inches, and a horizontal base of 14 inches. The trapezoid has a right angle at the bottom left corner. 2. **Goal:** The problem does not specify what to find explicitly, but typically with trapezoids, we might be asked to find the area or relate the sides. 3. **Formula for Area of a Trapezoid:** The area $A$ of a trapezoid is given by: $$ A = \frac{1}{2} (b_1 + b_2) h $$ where $b_1$ and $b_2$ are the lengths of the two parallel bases, and $h$ is the height. 4. **Identify Bases and Height:** Here, the bases are the two vertical sides $y$ and $x$ (since they are parallel vertical sides), and the height is the horizontal base 14 inches. 5. **Apply the formula:** $$ A = \frac{1}{2} (y + x) \times 14 $$ 6. **Simplify:** $$ A = 7 (y + x) $$ 7. **Interpretation:** The area of the trapezoid depends on the sum of the vertical sides $y$ and $x$. Without specific values for $x$ and $y$, this is the expression for the area. **Final answer:** $$ \boxed{A = 7 (y + x)} $$