Question

What is the area of the shaded region of the given $8\times5$ rectangle?

$4\dfrac{3}{5}$

$5$

$5\dfrac{1}{4}$

$6\dfrac{1}{2}$

$8$

Answer: D

Concepts:area decomposition triangle area

Difficulty rating: 1070

Solution:

We can split the region into $4$ triangles with bases of $1.$

All four triangles have base $1.$ Two have height $8\div2=4,$ and the other two have height $5\div2=\dfrac52.$

The sum of the areas of the triangles is $\begin{aligned} &2 \cdot \dfrac{1}{2} \left(1 \cdot \dfrac{5}{2}\right) \\ &\quad {}+ 2 \cdot \dfrac{1}{2} \left(1 \cdot 4\right) = 6\dfrac{1}{2} \end{aligned}$

Thus, the correct answer is D .

2016 AMC 10A Problem 11

Answer: D

Difficulty rating: 1070

Solution:

Problem 11 in Other Years