SOLUTION: Equilateral triangle △ABC has side length 2, M is the midpoint of segment AC, and C is the midpoint of BD. What is the area of △CDM? (please check the link below as it conta

Algebra.Com
Question 1151273: Equilateral triangle △ABC has side length 2, M is the midpoint of
segment AC, and C is the midpoint of BD. What is the area of
△CDM?
(please check the link below as it contains the image for the question)
https://i.imgur.com/g3InsY0.png

Found 2 solutions by ikleyn, jim_thompson5910:
Answer by ikleyn(53751)   (Show Source): You can put this solution on YOUR website!
.

HINT 1.  The area of the equilateral triangle is   square units, where "a" is its side length.

         So, in this case, the area of the equilateral triangle ABC is   = .



HINT 2.  The area of the triangle CDM is half the area of the triangle ABC.


Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Let's explore hint #2 that the tutor @ikleyn has provided.

Triangle ABC has base of BC = 2
Let h be the height of triangle ABC. It does not matter what h is for this thought experiment.
The area of triangle ABC is therefore, A = (1/2)*base*height = (1/2)*2*h = h.
Area of triangle ABC = h.

The base of triangle CDM is also 2, because C is the midpoint of BD, so BC = CD = 2.
The height of point M is half that of point A's height. Imagine that point A is (0, h). Through use of the midpoint formula, you'll find that the y coordinate of point M will be y = h/2.
So the height of triangle CDM is h/2.

area of triangle CDM = (1/2)*base*height
area of triangle CDM = (1/2)*2*(h/2)
area of triangle CDM = h/2
area of triangle CDM = (area of triangle ABC)/2

RELATED QUESTIONS

Each side of equilateral triangle ABC has a length of 8. AR is the altitude to BC. If... (answered by edjones)
C is the right angle in triangle ABC. D is the midpoint of side AC. E is the midpoint... (answered by lynnlo)
Given: segment BA congruent to segment BC, Ray BD bisects angle ABC Prove: D is the... (answered by solver91311)
ABC is a right angle isosceles triangle, angle BCA = 90, with BC as the base and AB as... (answered by Boreal,greenestamps)
In triangle ABC, E is the midpoint of AC and D is the midpoint of CB. If DF is parallel... (answered by ikleyn)
how do you do a proof that has a given:triangle ABC and triangle EDC, C is the midpoint... (answered by richard1234)
Given: E is the midpoint of line segment AC and line segment BD Prove: line segment AB... (answered by ikleyn)
given: B is the midpoint of AC C is the midpoint of BD prove: AB=... (answered by mananth)
Hi, I'm struggling with this test question that I'm really confused on: "In triangle... (answered by Boreal)