2016 AMC 8

Complete problem set with solutions and individual problem pages

Problem 2 Easy

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

  • A.

    12

  • B.

    15

  • C.

    18

  • D.

    20

  • E.

    24

Answer:A

Solution 1

Using the triangle area formula for triangles: A = \frac{bh}{2}, where A is the area, b is the base, and h is the height. This equation gives us A = \frac{4 \cdot 6}{2} = \frac{24}{2} =\boxed{\textbf{(A) } 12}.

 

Solution 2

A triangle with the same height and base as a rectangle is half of the rectangle's area. This means that a triangle with half of the base of the rectangle and also the same height means its area is one quarter of the rectangle's area. Therefore, we get \frac{48}{4} =\boxed{\textbf{(A) } 12}.

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