2016 AMC 10A Problem 11

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

Split the shaded region into four triangles

Use bases of length

1

with heights

4

and

\frac{5}{2}

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 .

Problem 11 in other years