Question

Suppose a square has side length s. How could you use the formula for the area of a trapezoid to find the area of the square?

A. For a square, h=b1=b2=s.

Substitute into the trapezoid area formula. You get A=12s(s+s)=12s(2s)=s^2.

This result is consistent with the formula for the area of a square.

B. For a square, s=b1=b2. Substitute into the trapezoid area formula. You get A=12s^2=s^2/2. This result is consistent with the formula for the area of a trapezoid.

Answer 1

A

Explanation:

The height of a square with side length s is h = s. The bases of a square with side length s are b1 = s and b2 = s. Using the formula for the area of a trapezoid, you would substitute h = b1 = b2 = s:

A = 1/2(b1 +b2)h

A = (1/2)(s +s)s = (1/2)(2s^2) = s^2

This is consistent with the formula for the area of a square.

This description matches choice A.

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Additional comment

You can also use the formula for the area of a trapezoid to find the area of a triangle. In that case, let b1 = b, b2 = 0, and you have ...

A = 1/2(b + 0)h = 1/2bh . . . . the formula for the area of a triangle.

In effect, when two sides are parallel, the area is the product of the distance between them and the average width of the figure. This is true even when one of them has zero length (as in a triangle).