1. ## area of trapezoid

ABCD is a square with area 16 sq meters. E and F are midpoints of sides AB and BC, respectively. What is the area of trapezoid AEFC?

A) 8 sq units B) 10 sq units C) 6 sq units D) 16 sq units
E) 12 sq units

2. Originally Posted by sri340
ABCD is a square with area 16 sq meters. E and F are midpoints of sides AB and BC, respectively. What is the area of trapezoid AEFC?

A) 8 sq units B) 10 sq units C) 6 sq units D) 16 sq units
E) 12 sq units
Hint: The two parallel sides have lengths of 2m and 4m respectively (why?) and the height is 4m (why?).

3. Hello, sri340!

Did you make a sketch?

$ABCD$ is a square with area 16 mē.
$E$ and $F$ are midpoints of sides $AB$ and $BC$, respectively.
What is the area of trapezoid $AEFC$ ?

. . A) 8 mē . . B) 10 mē . . C) 6 mē . . D) 16 mē . . E) 12 mē
Code:
              E
A *-------*-------* B
| *:::::|:*     |
|   *:::|:::*   |
|     *:|:::::* |
* - - - *:-:-:-:* F
| *     | *:::::|
|   *   |   *:::|
|     * |     *:|
D *-------*-------* C

With a few lines, we see that the square
. . is divided into 8 congruent right triangles.
The trapezoid occupies 3 of these triangles.

Therefore . . .