2021 AMC 12B Fall Problem 2

Attempt Problem 2 of the 2021 AMC 12B Fall below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 12B Fall solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

What is the area of the shaded figure shown below?

4

6

8

10

12

The shaded region is a large triangle with a triangular notch removed from its base

Both triangles have base

4

along the

x

-axis

The outer triangle has vertices

(1, 0),

(3, 5),

and

(5, 0),

giving base

4

and height

5,

so its area is

\tfrac12 \cdot 4 \cdot 5 = 10.

Removed from it is the triangle with vertices

(1, 0),

(3, 2),

and

(5, 0),

which has base

4

and height

2,

so area

\tfrac12 \cdot 4 \cdot 2 = 4.

The shaded area is

10 - 4 = 6.

Thus, the correct answer is B.

Problem 2 in other years