Final Answer:
The area of the trapezoid is 80 square inches.
Step-by-step explanation:
The area of a trapezoid is calculated using the formula A = (1/2)h(b1 + b2), where A is the area, h is the height, and b1 and b2 are the lengths of the two bases. In this trapezoid, the upper base (b1) is 7 inches, the lower base (b2) is 13 inches, and the height (h) is 6 inches. Plugging these values into the formula, we get A = (1/2)(6)(7 + 13) = 80 square inches.
Understanding the Geometry:
The trapezoid is divided into a right triangle, a rectangle, and another right triangle. The upper base of the rectangle aligns with the upper base of the trapezoid, while the bases of the rectangle and both triangles together form the lower base of the trapezoid. This division allows us to apply the area formula for a trapezoid accurately.
Application of the Area Formula:
The application of the area formula involves substituting the given dimensions into the equation, demonstrating the relationship between the geometric elements of the trapezoid. The result, 80 square inches, represents the total space enclosed by the trapezoid, incorporating the contributions of the rectangle and the two triangles.
Practical Implications:
Calculating the area of geometric shapes, such as trapezoids, is essential in various fields, including architecture, engineering, and design. It provides a quantitative measure of the space within the shape, aiding in planning and construction processes.
In conclusion, the final answer and explanation offer a concise and accurate solution to determine the area of the trapezoid, considering its geometric components.