Question

1. apply math models dan drew a trapezoid that has bases of length 12 inches and 20 inches and a height of 8 inches to represent a section of a stone patio. draw an example of the trapezoid that dan could have drawn. find its area.

Explanation:

Step1: Recall trapezoid area formula

The area $A$ of a trapezoid is given by:
$$A = \frac{1}{2}(b_1 + b_2)h$$
where $b_1$ and $b_2$ are the lengths of the two bases, and $h$ is the height.

Step2: Substitute given values

Substitute $b_1=12$, $b_2=20$, and $h=8$ into the formula:
$$A = \frac{1}{2}(12 + 20) \times 8$$

Step3: Simplify the expression

First calculate the sum inside the parentheses:
$$12 + 20 = 32$$
Then compute the product:
$$A = \frac{1}{2} \times 32 \times 8 = 16 \times 8 = 128$$

(Note for the drawing: Sketch a quadrilateral with one side 12 inches, a parallel side 20 inches, and the perpendicular distance (height) between these two sides equal to 8 inches. The non-parallel sides can be slanted at any consistent angle.)

Answer:

The area of the trapezoid is 128 square inches.