Problem:
Equilateral △ABC has side length 2,M is the midpoint of AC, and C is the midpoint of BD. What is the area of △CDM?
Answer Choices:
A. 22
B. 43
C. 23
D. 1
E. 2
Solution:
Drop MQ perpendicular to BC. Then △MQC is a 30−60−90∘ triangle, so MQ=3/2, and the area of △CDM is
21(2⋅23)=(C)23
OR
Triangles ABC and CDM have equal bases. Because M is the midpoint of AC, the ratio of the altitudes from M and from A is 1/2. So the area of △CDM is half of the area of △ABC. Since
