Question

In rectangle $ABCD,$ $AB=6$ and $AD=8.$ Point $M$ is the midpoint of $\overline{AD}.$ What is the area of $\triangle AMC?$

$12$

$15$

$18$

$20$

$24$

Answer: A

Concepts:triangle area midpoint

Difficulty rating: 450

Small Hint:

Since $M$ is the midpoint of $\overline{AD}$ , find $AM$ .

Big Hint:

Use $AM$ as the base and the rectangle’s vertical side length as the height.

Video solution:

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Written solution:

Since $M$ is the midpoint of $\overline{AD},$ the base $AM$ has length $4.$ The altitude from $C$ to $\overline{AM}$ has length $AB=6.$ The area is therefore $\dfrac{1}{2} \cdot 4 \cdot 6 = 12.$

Thus, A is the correct answer.

2016 AMC 8 Problem 2