Question

In rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB=3 and BC=2, what is the area of the shaded region? Write your answer as a decimal, if necessary. Do not include units in your answer.

Answer 1

Answer:

The area of the shaded region is 3.

Step-by-step explanation:

Since point E lies halfway between AB and BC, the area of the shaded region (As) consists of two identical triangles with base equal to AB and height equal to half the measure of BC:

$A_s=2 * A_t$

Where At is the area of each triangle.

$\displaystyle A_t=\frac{AB*BC/2}{2}$

$\displaystyle A_t=\frac{AB*BC}{4}$

We know AB=3 and BC=2, thus:

$\displaystyle A_t=\frac{3*2}{4}=\frac{6}{4}$

Simplifying:

$\displaystyle A_t=\frac{3}{2}$

Finally:

$\displaystyle A_s=2 * \frac{3}{2}$

$A_s=3$

The area of the shaded region is 3.

Note the area of the shaded region is half the area of the rectangle.