Question

The twelve-sided figure shown has been drawn on $1 \text{ cm}\times 1 \text{ cm}$ graph paper. What is the area of the figure in $\text{cm}^2?$

$12$

$12.5$

$13$

$13.5$

$14$

Answer: C

Concepts:area decomposition triangle area

Difficulty rating: 770

Video solution:

Click to load, then click again to play

Written solution:

To solve for the area of the figure, we separate the compound shape into parts that are easier to work with, as such:

As is now clear, there is the center $3 \times 3$ square, with $4$ smaller shaded triangles surrounding it.

The area of the square is $3 \cdot 3 = 9.$ The other triangles each have a base of $2$ and a height of $1,$ so their area is equal to $\dfrac{bh}{2} = \dfrac{2\cdot 1}{2} =1 .$ There are $4$ of these triangles, so their total area is $1\cdot 4 = 4.$

Therefore, the total area is $9+4 = 13.$

Thus, the correct answer is C.

2018 AMC 8 Problem 4

Answer: C

Difficulty rating: 770

Video solution:

Written solution:

Problem 4 in Other Years