Question

Question

In rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB = 7 and
BC= 6, what is the area of the shaded region? Write your answer as a decimal, if necessary. Do not include units in your
answer.
evious
D
E
B

Answer 1

I believe the area would be 22

Answer 2

The area of the shaded region is 21.

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.

`A_t=(AB* BC/2)/(2)`

`A_t=(AB* BC)/(4)`

We know AB=7 and BC=6, thus:

`A_t=(7*6)/(4) =(42)/(4)`

Simplifying:

`A_t=(21)/(2)`

Finally:

`A_s=2*(21)/(2)`

`A_s=21`

The area of the shaded region is 21.

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