The area of a trapezoid with bases b1 and b2 and height h is

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Multiple Choice

The area of a trapezoid with bases b1 and b2 and height h is

Explanation:
The area of a trapezoid comes from using the height and the two bases together in a way that accounts for how the width changes from one base to the other. The width across the shape varies linearly from b1 to b2, so the effective width is the average of the two bases, which is (b1 + b2)/2. Multiply that by the height h (the perpendicular distance between the bases) to get the area: h times (b1 + b2)/2, which is (1/2) h (b1 + b2). This also makes sense when the trapezoid becomes a rectangle (if b1 equals b2, the formula reduces to base times height). If you omit the 1/2, you’d overestimate the area; if you multiply the bases together, you’re not reflecting how width varies with height; and pi r^2 is the area formula for a circle, not a trapezoid.

The area of a trapezoid comes from using the height and the two bases together in a way that accounts for how the width changes from one base to the other. The width across the shape varies linearly from b1 to b2, so the effective width is the average of the two bases, which is (b1 + b2)/2. Multiply that by the height h (the perpendicular distance between the bases) to get the area: h times (b1 + b2)/2, which is (1/2) h (b1 + b2). This also makes sense when the trapezoid becomes a rectangle (if b1 equals b2, the formula reduces to base times height). If you omit the 1/2, you’d overestimate the area; if you multiply the bases together, you’re not reflecting how width varies with height; and pi r^2 is the area formula for a circle, not a trapezoid.

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