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.

  A

Step-by-step 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.

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).

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap