Question

Find the area of the trapezoid by decomposing it into other shapes.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the area of a trapezoid, we can decompose it into a rectangle and two right triangles.

Let's consider the following trapezoid:

```
/------\
/ \
/__________\
```

We can extend the top side of the trapezoid to create a rectangle as shown below:

```
/------\
/ \
/__________\
```
```
/------\
/ \
/----------\
```

The area of this rectangle is equal to the product of its length (which is the same as the length of the bottom side of the trapezoid) and its width (which is the same as the height of the trapezoid).

Now let's remove the two right triangles from the top corners of the trapezoid:

```
/------\
/ \
/__________\
```
```
/------\
/ | \
/----|-----\
```

The area of each right triangle is equal to half the product of its base (which is the difference between the lengths of the top and bottom sides of the trapezoid) and its height (which is the same as the height of the trapezoid).

Therefore, by decomposing the trapezoid into a rectangle and two right triangles, we can find its total area by adding the areas of these individual shapes:

Area of trapezoid = Area of rectangle + 2 x Area of right triangle

Note: If the trapezoid has parallel sides of length a and b, and height h, the area of the trapezoid can also be directly calculated using the formula:

Area = (a + b) x h / 2