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MathNet 2020 — Math Olympiad Vault — Part 05 Question 37

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 05

Question 37

In cube $ABCDEFGH$ of edge length $6~\mathrm{cm}$, point $M$ is the midpoint of $EF$.

Question illustration

a) Find the area of triangle $AMH$.

b) Find the volume of pyramid $AMHE$. (The volume of a pyramid is one third of the product of the base area and the corresponding height.)

c) Find the height corresponding to base $AMH$.