Question

In rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB=10 and BC=5, what is the area of the shaded region? Write your answer as a decimal if necessary.

Answer 1

Answer:

The area of the shaded region is 25 square units

Step-by-step explanation:                                

see the attached figure to better understand the problem

we know that                  

The area of the shaded region is equal to the area of triangle ABE plus the area of triangle CDE      

Remember that the area of triangle is equal to

$A=\frac{1}{2}bh$

where                

b is the base

h is the height              

Find the area of triangle ABE                                              

$b=AB=10\ units$                        

$h=\frac{BC}{2}=\frac{5}{2}=2.5\ units$

substitute the values                                

$A=\frac{1}{2}(10)(2.5)=12.5\ units^2$                

Find the area of triangle CDE

$b=CD=AB=10\ units$                          

$h=\frac{BC}{2}=\frac{5}{2}=2.5\ units$

substitute the values                    

$A=\frac{1}{2}(10)(2.5)=12.5\ units^2$                                    

Find the area of the shaded region                                      

$A=12.5\ units^2+12.5\ units^2=25\ units^2$