Question

The bases of an isosceles trapezoid are represented by 4x and 2x.. The height of the trapezoid is represented by (x − 6). Which polynomial expression BEST represents the area of the trapezoid?

A) 3x2 − 18x
B) 3x2 + 18x
C) 3x − 18
D) 6x2 + 36x

Answer 1

Explanation:

3x2 + 8x + 4

A =

1

2

(b1 + b2)(height)

A =

1

2

(3x + 3x + 4)(x + 2)

A =

1

2

(6x + 4)(x + 2)

A =

1

2

(6x2 + 16x + 8)

A = 3x2 + 8x + 4

The answer is A

Answer 2

The area of a trapezoid is calculated by the equation,
A = 0.5(b₁ + b₂)h
where b₁ and b₂ are the bases and h is the height. When we substitute the given expression for the dimensions in the given,
A = 0.5(4x + 2x)(x - 6)
A = 0.5(6x)(x - 6) = 3x² - 18
Thus, the answer is letter A.