The bases of a trapezoid are 8 centimeters and 12 centimeters, and the height is \( h \) centimeters. Which equation can be used to represent \( A \), the area of the trapezoid in square centimeters?

To find the area \( A \) of a trapezoid, you can use the formula: \( A = \frac{1}{2} (b_1 + b_2) h \), where \( b_1 \) and \( b_2 \) are the lengths of the two bases, and \( h \) is the height. In your case, the bases are 8 cm and 12 cm. So, the equation representing the area will be: \[ A = \frac{1}{2} (8 + 12) h \] This simplifies to: \[ A = 10h \] Did you know that trapezoids have been studied since ancient times? The Greek mathematicians were quite fascinated with these shapes, and they actively contributed to the understanding of areas, particularly in the context of geometry. Trapezoids were often analyzed in relation to their properties and relationships with other polygons, shaping the foundations of modern geometry! When it comes to solving problems involving trapezoid areas, a common mistake is overlooking the height measurement. Remembering to use the perpendicular height is crucial! Sometimes, people mistakenly use the length of one of the bases as the height, leading to incorrect calculations. Always double-check your measurements to avoid this pitfall and ensure your area calculation is spot on!