Question

In the rectangle ABDF above, C and E are midpoints of sides line ED and line DF, respectively, what fraction of the areas of the rectangle is shaded?

Answer 1

Is shaded 5/8 of the area of the rectangle

Explanation:

see the attached figure to better understand the problem

we know that

The area of triangle ABC represent 1/4 of the total area

The area of triangle CDE represent 1/8 of the total area

The shaded region is composed by one triangle equal to triangle ABC and three triangles equal to triangle CDE

so

The area of the shaded region is equal to

`(1/4)(1)+(1/8)(3)=(1/4)+(3/8)=(2/8)+(3/8)=5/8`

therefore

Is shaded 5/8 of the area of the rectangle