2016 AMC 12A Problem 8

Question

What is the area of the shaded region of the given

8\times 5

rectangle?

4\tfrac{3}{4}

5

5\tfrac{1}{4}

6\tfrac{1}{2}

8

Answer: D

Concepts:triangle area symmetry

Difficulty rating: 1350

Small hint:

Every drawn segment passes through the center of the rectangle

Big hint:

The main diagonal splits the shaded region into four triangles, each with base

1

Solution:

The diagonal of the rectangle from the upper-left corner to the lower-right corner divides the shaded region into four triangles, all meeting at the center of the rectangle.

Two of these triangles have a horizontal base of length

1

and altitude

\frac12\cdot 5=\frac52,

and the other two have a vertical base of length

1