Tiling a Pentagon with a Polyiamond

Introduction

A polyiamond is a plane figure formed by joining equal equilateral triangles edge to edge.

A pentagon is a plane figure with 5 sides. There are four types of polyiamond pentagons: D, M, P, and Q. See below under Moniamond for examples.

Here I show the smallest known pentagon of each type that can be tiled with a given polyiamond with up to 8 cells. If you find a smaller solution or solve an unsolved case, please write.

Carl Schwenke and Johann Schwenke provided solutions.

A polyiamond with equal numbers of up and down cells cannot tile a pentagon. Such polyiamonds are not shown.

For heptiamonds and octiamonds, I show only polyiamonds with at least one solution.