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

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Multiple Choice

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

Explanation:
The area of a trapezoid is found by multiplying the height by the average of the two parallel bases. With bases b1 and b2 and height h, this becomes A = h × (b1 + b2)/2, which is the same as A = (1/2) h (b1 + b2). This shows that you take the average width across the height (since the width changes from b1 to b2) and scale it by how tall the shape is. If you used h(b1 + b2) you’d be missing the necessary division by 2, giving an area too large by a factor of 2. The option 1/2 b1 b2 leaves out the height entirely, so it doesn’t reflect how area depends on how tall the trapezoid is. pi r^2 is the formula for a circle, not a trapezoid. Therefore the correct expression is 1/2 h (b1 + b2).

The area of a trapezoid is found by multiplying the height by the average of the two parallel bases. With bases b1 and b2 and height h, this becomes A = h × (b1 + b2)/2, which is the same as A = (1/2) h (b1 + b2). This shows that you take the average width across the height (since the width changes from b1 to b2) and scale it by how tall the shape is.

If you used h(b1 + b2) you’d be missing the necessary division by 2, giving an area too large by a factor of 2. The option 1/2 b1 b2 leaves out the height entirely, so it doesn’t reflect how area depends on how tall the trapezoid is. pi r^2 is the formula for a circle, not a trapezoid. Therefore the correct expression is 1/2 h (b1 + b2).

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