Question

In rectangle ABCD, point E lies halfway between sides AB and CD and halfway between sides AD and BC. If AB = 9and BC = 10, what is the area of the shaded region? Write your answer as a decimal if necessary.

Answer 1

45 square units.

Explanation:

Given that point E is halfway between AD and BC; and

• AB=9

,

• BC=10

The diagram showing this is attached below:

The unshaded region is divided into two triangles (BEC and AED) each having the dimensions:

• Base = 10

,

• Height = 4.5

Therefore, the area of the shaded region will be:

`\begin{gathered} \text{Area of shaded region=Area of Rectangle-Area of Unshaded Region} \\ =(10*9)-2((1)/(2)*10*4.5) \\ =90-45 \\ =45\text{ square units.} \end{gathered}`

The area of the shaded region is 45 square units.